HSN.Q.A.3Common CoreMathNumber and QuantityGrades 9-12
HSN.Q.A.3: Choosing an Appropriate Level of Accuracy
In plain English: HSN.Q.A.3 is the Common Core number and quantity standard that asks students to report measured and computed quantities with a level of accuracy their measurements can support. Students find the precision of a measuring tool, track the possible error through a calculation, and round results so they claim neither more nor less than the data allow. It is usually taught in Algebra I.
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Common Core State Standards for Mathematics · Domain: Quantities (Q) · Cluster: Reason quantitatively and use units to solve problems. Also written as HSN-Q.A.3 or N-Q.3 · Official standard
Every measurement is an interval, not a single number. A length read as 3.4 m on a tape marked in tenths of a meter could be anything from 3.35 m to 3.45 m. HSN.Q.A.3 asks students to use that fact when they report results: the number of digits in an answer should match what the measuring tools and the situation can support.
Students first find the precision of a tool and the greatest possible error of a reading. They then carry measurements through a calculation, find the smallest and largest possible results, and round the answer to digits the range supports. The lesson ends with context: a machinist, a nurse, a crowd estimator and a recipe writer each need a different level of accuracy, and students justify the choice for each.
Learning Objectives
By the end of this lesson, students will be able to:
State the precision of a measuring tool and the greatest possible error of a reading
Write a measurement as an interval of possible true values
Find the smallest and largest possible values of a quantity computed from measurements
Report a measured or computed quantity with a level of accuracy that the measurements and the context support, and explain the choice
Prior Knowledge Required
Students should already be comfortable with:
Rounding decimals to any place 5.NBT.A.4
Area and volume of rectangles, prisms and other figures 7.G.B.6
Solving multi-step problems with decimals and checking reasonableness 7.EE.B.3
Choosing units of appropriate size, including in scientific notation 8.EE.A.4
Show three reports of the same desk width and ask students to rank how much each one claims.
Warm-Up Prompt
"Three students measured the same desk with a meter stick marked in millimeters. They reported 76 cm, 75.8 cm and 75.83 cm. Which report does the meter stick support? What would you need to believe to trust 75.83 cm?"
A millimeter mark is 0.1 cm, so the stick reads to the nearest 0.1 cm. The report 75.8 cm means the true width is between 75.75 cm and 75.85 cm. The report 75.83 cm claims hundredths of a centimeter, which the stick cannot show, and 76 cm throws away a digit the tool did measure. Introduce the word precision for the smallest unit a tool reads.
Direct Instruction20 minutes
Part 1: From a reading to an interval. Model this routine with every example:
Find the precision: the smallest unit the tool reads, such as 1 mm, 2 g or 0.1 s.
State the greatest possible error: half of that unit. A reading of 3.4 m to the nearest 0.1 m has an error of at most 0.05 m.
Write the interval: reading minus the error to reading plus the error.
Compute with the full readings, then compute again with the smallest and the largest possible inputs to get the range of the result.
Round to what the range supports, and say it in words: "about 9.2 m², between 8.9 and 9.5 m²."
Precision and greatest possible error
A kitchen scale reads to the nearest 2 g and shows 346 g. What masses are possible?
Equation: Greatest possible error = 2 ÷ 2 = 1 g, so the true mass is from 345 g to 347 g.
Accuracy of a computed area
A garden bed is measured to the nearest 0.1 m as 3.4 m by 2.7 m. The calculator gives 3.4 × 2.7 = 9.18 m².
Equation: Smallest: 3.35 × 2.65 = 8.8775 m². Largest: 3.45 × 2.75 = 9.4875 m². Even the tenths digit is uncertain, so report about 9.2 m², not 9.18 m².
An estimate should not look like a count
Organizers estimate a crowd on an 8,000 m² plaza by sampling: about 2.3 people per square meter, estimated to the nearest 0.1.
Equation: 2.3 × 8,000 = 18,400, but 2.25 × 8,000 = 18,000 and 2.35 × 8,000 = 18,800. Report "about 18,000 to 19,000 people," since 18,400 reads like an exact count.
Timing limits the accuracy of a rate
A 100 m sprint is hand-timed at 12.4 s. Hand timing can be off by about 0.2 s. Find the average speed.
Equation: 100 ÷ 12.4 ≈ 8.0645 m/s, but 100 ÷ 12.6 ≈ 7.94 and 100 ÷ 12.2 ≈ 8.20. Report about 8 m/s (between 7.9 and 8.2 m/s).
Converting units does not add accuracy
A student's height is measured as 68 inches to the nearest inch. Convert to centimeters (1 in = 2.54 cm).
Equation: 68 × 2.54 = 172.72 cm, but the true height is 67.5 to 68.5 in, or 171.45 to 173.99 cm. Report about 173 cm, not 172.72 cm.
Part 2: Why computed results need care. Use Diagram 1 to show that a reading is an interval and that a finer tool gives a narrower one. Then use Diagram 2 to show the garden bed: the smallest and largest possible rectangles differ by more than half a square meter, so the calculator's hundredths digit means nothing. Point out that errors grow when measurements are multiplied: each side is uncertain by about 1.5% to 1.9%, and the area by about 3.3%.
Part 3: Context decides how much accuracy is needed. Accuracy costs time and better tools, so the right level depends on the use. A surveyor marking a property line needs centimeters; a recipe needs about a quarter cup; a crowd estimate needs the nearest thousand. Students should also avoid the opposite mistake: rounding a careful measurement so far that useful information is lost, such as reporting a lab mass of 47.46 g as "about 50 g."
Guided Practice15 minutes
Pairs work three problems. For each, they write the precision, the interval or bounds, and a final report in words.
Thermometer. A thermometer reads to the nearest 0.5 °C and shows 37.5 °C. (Error up to 0.25 °C, so 37.25 °C to 37.75 °C.)
Perimeter. A square tile's side is measured as 30 cm to the nearest centimeter. Find the perimeter and its range. (120 cm, from 4 × 29.5 = 118 cm to 4 × 30.5 = 122 cm.)
Speed. A toy car rolls 2.40 m, measured to the nearest centimeter, in 3.2 s, timed to the nearest 0.1 s. (2.40 ÷ 3.2 = 0.75 m/s; bounds 2.395 ÷ 3.25 ≈ 0.737 and 2.405 ÷ 3.15 ≈ 0.763, so about 0.75 m/s, between 0.74 and 0.76 m/s.)
Watch for pairs who add the error to the result instead of recomputing with the bounds, who use the full unit (0.1) instead of half of it as the error, and who pair the smallest distance with the largest time only by accident: for a quotient, the smallest result comes from the smallest numerator and the largest denominator.
Independent Practice10-15 minutes
Students work alone and write a one-sentence report for each result.
A bathroom scale reads to the nearest 0.5 lb and shows 152.5 lb. Give the interval of possible weights. (152.25 lb to 152.75 lb.)
A room is measured as 4.2 m by 3.6 m to the nearest 0.1 m. The calculator shows 15.12 m². Find the bounds and write a report. (4.15 × 3.55 ≈ 14.73 and 4.25 × 3.65 ≈ 15.51, so about 15 m², between 14.7 and 15.5 m².)
On a map with a scale of 1 cm to 2.5 km, a road measures 6.3 cm to the nearest millimeter. How long is the road? (15.75 km, but between 15.625 and 15.875 km, so about 16 km, or 15.6 to 15.9 km.)
A fitness app uses GPS that is accurate to about 0.05 mile and reports a walk of 3.2817 miles. Which is the better report, "3.2817 miles" or "about 3.3 miles"? Explain. (About 3.3 miles: with an error of up to 0.05 mile, the hundredths and thousandths digits carry no information.)
Closure5 minutes
Exit ticket: A board measured as 2.45 m to the nearest centimeter is cut into 3 equal pieces (ignore the width of the saw cut). The calculator shows 0.816666... m. Write a report of each piece's length and justify the number of digits. (Bounds 2.445 ÷ 3 = 0.815 m and 2.455 ÷ 3 ≈ 0.818 m, so about 81.7 cm, between 81.5 and 81.8 cm.)
Differentiation Strategies
For Struggling Students
Give a three-column organizer: reading, greatest possible error, interval. Fill in the first row together before students work alone
Use physical rulers with only centimeter marks and then millimeter marks so students see where the uncertainty comes from
For computed results, provide the bounds already written as two calculations ("smallest × smallest", "largest × largest") and ask only for the final report
For Advanced Students
Compare the percent error of a circle's measured radius with the percent error of its computed area, and explain the pattern
Look up the tolerance printed on a manufactured part, such as a resistor band or a bolt package, and explain what it says about the part's possible sizes
Compare the bounds method with significant-figure rules on three examples and find a case where the two give different reports
Assessment Guidance
What to Look For
Strong work states the precision of each tool, writes the interval without being asked, and reports a final answer in words with a range or "about." Watch for students who copy every calculator digit, who treat the full marking interval as the error instead of half of it, and who round a computed answer to the same decimal place as the inputs without checking the bounds. Ask each student to explain one report in terms of the tool: "the tape only reads tenths of a meter, so..."
02
Classroom Activities
3 Activities
1
Measure It Three Ways
20 minGroups of 3
Each group measures the width of the same textbook with three tools: hand spans, a ruler marked only in centimeters, and a ruler marked in millimeters. For each tool they record the reading, the precision, the greatest possible error and the interval of true values.
Recording Sheet (sample row)
Tool
Reading
Precision
Greatest possible error
Interval
Centimeter ruler
27 cm
1 cm
0.5 cm
26.5 cm to 27.5 cm
Millimeter ruler
27.3 cm
0.1 cm
0.05 cm
27.25 cm to 27.35 cm
Procedure
Each student measures separately and records the reading before seeing the others
The group writes the interval for each tool and checks whether the three students' intervals overlap
Groups post their millimeter readings on the board; the class checks whether all readings fit within one or two millimeters
Discussion Questions
Why do the hand-span readings disagree so much more than the ruler readings?
If two readings from the millimeter ruler differ by 2 mm, is one of them wrong?
Which tool would you use to order a book cover? To tell a friend how big the book is?
2
Too Precise, Too Rough or Just Right
20 minPairs
Pairs sort 8 report cards into three piles: too precise, too rough, or appropriate. For each card they name the tool or method, its precision, and a better report if one is needed.
The 8 Report Cards (suggested sort in parentheses)
A hallway measured with a tape marked in centimeters is reported as 38.2649 m. (Too precise: the tape supports 38.26 m.)
A stadium crowd counted at the turnstiles is reported as 41,208. (Appropriate: turnstiles count every person, so the exact number is supported.)
A protest crowd estimated from an aerial photo is reported as 41,208. (Too precise: report about 41,000 or a range.)
A pharmacist weighs a powder on a scale that reads to 0.001 g and records "about 1 gram." (Too rough for the context: record the reading, such as 1.004 g.)
An electronic timing system reports a 1,500 m race time as 4:12.37. (Appropriate: electronic timing reads hundredths of a second.)
A student averages three test scores of 82, 88 and 90 and reports 86.666667. (Too precise: 86.7 is enough for a grade book.)
A recipe converted from 1 cup of milk asks for 236.588 mL. (Too precise: a kitchen measuring cup supports about 240 mL.)
A 2 hour 47 minute drive is reported as "about 3 hours" in a message to a friend. (Appropriate for the purpose, though too rough for a timesheet.)
Procedure
Pairs sort the cards without discussion first, then compare and settle disagreements
For each card in the "too precise" or "too rough" pile, pairs write a corrected report on the back
Two pairs join and explain one card where they changed their minds
Discussion Questions
The two crowd cards show the same number. Why is one appropriate and the other not?
Who decides how accurate a report must be: the tool, the person using the number, or both?
3
Bounds Challenge
25 minGroups of 3-4
Groups measure a rectangular object in the room (a door, a whiteboard, a desk top) to the nearest centimeter, compute its area, find the smallest and largest possible areas, and write a report. Then they compare with another group that measured the same object.
Sample Record
Door: 203 cm by 81 cm, each to the nearest centimeter. Calculator: 203 × 81 = 16,443 cm². Smallest: 202.5 × 80.5 ≈ 16,301 cm². Largest: 203.5 × 81.5 ≈ 16,585 cm². Report: about 16,400 cm², or 1.64 m², with a true value between about 1.63 and 1.66 m².
Procedure
Measure each side twice with different group members; if the readings differ, measure again
Compute the area and the bounds, and write a report with a range
Compare with the other group: do the two ranges overlap? If not, find the measuring error
Challenge Variation
Measure the diameter and height of a can to the nearest millimeter, compute the volume with V = πr²h and its bounds, and compare the report with the volume printed on the label.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Reading Stands for an Interval
Two tape measures read the same length, drawn to scale from 3.30 m to 3.50 m. A tape marked every 0.1 m supports "3.4 m," meaning 3.35 m to 3.45 m. A tape marked every 0.01 m supports "3.42 m," an interval ten times narrower.
Diagram 2: Bounds on the Area of a Measured Rectangle
The garden bed from Example 2 drawn to scale at 100 px per meter. The dotted rectangle is the smallest bed the measurements allow, the solid one is the bed as measured, and the dashed one is the largest. The true area can be anywhere from about 8.9 m² to 9.5 m².
04
Homework Assignment
~30 min
HSN.Q.A.3 Homework: Level of Accuracy
Directions: For each measurement, state the precision and the greatest possible error. For computed quantities, find the smallest and largest possible values before you round. End every problem with a report in words that a reader can trust.
Part 1: Precision and Possible Error (Problems 1-2)
A digital thermometer reads to the nearest 0.1 °F and shows 98.6 °F. A dial thermometer reads to the nearest 2 °F and shows 98 °F. For each, give the greatest possible error and the interval of possible true temperatures. Which reading is more precise?
A postal scale reads to the nearest 0.02 kg. Package 1 reads 2.36 kg and Package 2 reads 1.18 kg. Give the interval for each package and the interval for their total mass.
Part 2: Accuracy of Computed Quantities (Problems 3-5)
A poster is measured as 61 cm by 91 cm, each to the nearest centimeter. The calculator gives an area of 5,551 cm². Find the smallest and largest possible areas and write an appropriate report.
A cyclist rides 18.4 km, measured to the nearest 0.1 km, in 47 minutes, timed to the nearest minute. Find the average speed in km/h, find its bounds, and write an appropriate report. Explain which combination of distance and time gives each bound.
A cylindrical water tank has radius 1.2 m and height 2.5 m, each measured to the nearest 0.1 m. Use V = πr²h to find the volume and its bounds. Explain why the report should be less precise than the measurements.
Part 3: Choosing Accuracy for the Context (Problem 6)
Choose an appropriate level of accuracy and explain it: (a) the number of people at a 5K fun run, estimated from photos; (b) the diameter of a bolt that must fit a hole drilled to 12.00 mm; (c) the average daily screen time of 30 students who each reported their time to the nearest half hour, where the responses add up to 131 hours.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Precision and Error
Precision and greatest possible error correct for every measurement
One error value wrong, such as the full unit used instead of half
Precision or error missing
Bounds
Smallest and largest results computed with the correct combinations of inputs
Bounds attempted with one incorrect combination
No bounds
Final Report
Rounded to digits the bounds support, with a unit and a range or "about"
Reasonable rounding without justification
Every calculator digit copied, or rounded so far that information is lost
Context
Explains why the chosen accuracy fits the use of the number
Choice stated without reasons
No reference to context
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Choose an answer or write your own, then open the explanation. Your score tracks the multiple-choice questions, and Reset quiz starts the quiz over.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A ruler is marked in millimeters. Which reading of a pencil's length does the ruler support?
Answer: C
Millimeter marks are 0.1 cm apart, so the ruler reads to the nearest 0.1 cm: 14.3 cm. Choices B and D claim thousandths or hundredths of a centimeter that the ruler cannot show. Choice A throws away a digit the ruler does measure.
Question 2 of 20 · Multiple Choice
A length is measured as 8.6 cm to the nearest 0.1 cm. Which interval contains the true length?
Answer: B
The greatest possible error is half of 0.1 cm, or 0.05 cm, so the length is from 8.55 to 8.65 cm. Choice A uses the full 0.1 cm as the error. Choice C assumes the reading was rounded down. Choice D uses an error of 0.01 cm, which would need a finer tool.
Question 3 of 20 · Multiple Choice
A scale reads to the nearest 10 g and shows 470 g. What is the greatest possible error of this reading?
Answer: D
The greatest possible error is half the precision: 10 ÷ 2 = 5 g, so the mass is from 465 g to 475 g. Choice A is the full precision, not half of it. Choices B and C would apply to scales that read to the nearest 2 g or 1 g.
Question 4 of 20 · Multiple Choice
A square patio's side is measured as 5.0 m to the nearest 0.1 m. What is the range of possible areas?
Answer: A
The side is from 4.95 m to 5.05 m, so the area is from 4.95² = 24.5025 m² to 5.05² = 25.5025 m². Choice B treats the area as uncertain by only 0.1 m², as if the error of each side did not grow when the sides are multiplied. Choice C ignores the measurement error. Choice D is wider than the measurements allow.
Question 5 of 20 · Multiple Choice
A calculator shows 17.3205081 cm for a length computed from sides measured to the nearest 0.1 cm. Which report is most appropriate?
Answer: B
The inputs are good to about 0.1 cm, so the result should be reported to about the same place, 17.3 cm. Choices A and D copy digits the measurements cannot support. Choice C rounds so far that the information the ruler did give is lost.
Question 6 of 20 · Multiple Choice
Which situation needs the greatest level of accuracy?
Answer: D
An engine part that must fit another part can fail if it is off by a fraction of a millimeter, so it needs the finest accuracy. Directions (choice A), a poster (choice B) and a parade count (choice C) are fine with rough values.
Question 7 of 20 · Multiple Choice
A trip of 312 miles, read from the odometer to the nearest mile, took 5 hours 10 minutes, timed to the nearest 10 minutes. The calculator gives 60.387 mi/h. Which report fits the measurements?
Answer: C
The time is between 5 h 5 min and 5 h 15 min, so the speed is between 311.5 ÷ 5.25 ≈ 59.3 and 312.5 ÷ 5.083 ≈ 61.5 mi/h. Only "about 60" is supported. Choices A and B claim thousandths and hundredths. Choice D rounds so far that it is wrong.
Question 8 of 20 · Multiple Choice
Kim measures a table as 1.5 m. Lee measures the same table as 1.52 m. Which statement is true?
Answer: A
Lee reports to the nearest 0.01 m and Kim to the nearest 0.1 m, so Lee's is more precise. The two do not contradict (choice C): 1.52 lies in Kim's interval of 1.45 to 1.55 m. Choice D confuses precision with accuracy; a precise reading can still be wrong if the tool is misused.
Question 9 of 20 · Multiple Choice
A room is measured as 5.2 m by 4.1 m, each to the nearest 0.1 m. What is the largest possible area?
Answer: B
The largest room is 5.25 m by 4.15 m, and 5.25 × 4.15 = 21.7875 m². Choice A is the area as measured. Choice C is the smallest possible area, 5.15 × 4.05. Choice D is not a product of any allowed side lengths.
Question 10 of 20 · Multiple Choice
A survey estimates a city's population as 86,000, give or take 3,000. A report says the city has 86,417 residents. What is wrong with the report?
Answer: D
An estimate that could be off by 3,000 cannot support the digits 417. "About 86,000" or "83,000 to 89,000" matches the survey. Choice A confuses more digits with more accuracy. Choices B and C change the estimate for no reason.
Question 11 of 20 · Multiple Choice
A length of 12 inches, measured to the nearest inch, is converted to 30.48 cm. Which report keeps the accuracy of the original measurement?
Answer: C
The length is 11.5 to 12.5 in, which is 29.21 to 31.75 cm, so only "about 30 cm" is supported. Choice A keeps the digits of the conversion, not of the measurement, and choice B claims an error of 0.01 cm when the real one is up to 1.27 cm. Choice D still claims tenths of a centimeter.
Question 12 of 20 · Multiple Choice
A bag of 7 apples weighs 3 lb on a scale that reads to the nearest pound. The calculator gives 0.428571 lb per apple. Which report fits?
Answer: A
The bag weighs 2.5 to 3.5 lb, so the average apple weighs between 2.5 ÷ 7 ≈ 0.36 lb and 3.5 ÷ 7 = 0.5 lb. Even the tenths digit is uncertain, so "about 0.4 lb" is the most the scale supports. Choices B, C and D all claim more than the scale can show.
Question 13 of 20 · Multiple Choice
Timing one swing of a pendulum with a hand stopwatch gives a poor result because reaction time is about 0.2 s. Which method gives a more accurate time for one swing?
Answer: A
The reaction error of about 0.2 s is shared by all 20 swings, so each swing's time is uncertain by only about 0.01 s. Choice B shows more digits but does not reduce the reaction error. Choice C adds digits without adding accuracy. Choice D keeps the same error.
Question 14 of 20 · Multiple Choice
A lab report gives an object's mass as 12.0 g. What does the zero after the decimal point tell the reader?
Answer: B
Writing 12.0 reports a tenths digit that was measured, so the mass is 12.0 ± 0.05 g. Choice A ignores that a reported zero carries information. Choice C forgets that every measurement has an error. Choice D describes a report of "12 g."
Question 15 of 20 · Short Answer
A digital kitchen scale reads to the nearest gram and shows 128 g. Give the greatest possible error and the interval of possible masses.
The greatest possible error is half of 1 g, 0.5 g, so the mass is from 127.5 g to 128.5 g.
Question 16 of 20 · Short Answer
A table top is measured as 1.8 m by 0.9 m, each to the nearest 0.1 m. Find the calculated area, the smallest and largest possible areas, and an appropriate report.
As measured: 1.8 × 0.9 = 1.62 m². Smallest: 1.75 × 0.85 ≈ 1.49 m². Largest: 1.85 × 0.95 ≈ 1.76 m². The true area could be anywhere in a range about 0.27 m² wide, so report about 1.6 m² (between about 1.5 and 1.8 m²).
Question 17 of 20 · Short Answer
Five students' heights, each measured to the nearest centimeter, are 162, 158, 171, 165 and 169 cm. A student reports the mean as 165.0000 cm. Is this report appropriate? Explain.
The mean is 825 ÷ 5 = 165 cm, but writing 165.0000 claims accuracy to 0.0001 cm when each height is known only to within 0.5 cm. Report about 165 cm. The extra zeros are not "free": they tell the reader the measurements were far more precise than they were.
Question 18 of 20 · Short Answer
A water bottle label says 500 mL. A student pours the water into a graduated cylinder marked every 2 mL and reads 496 mL. Does the measurement show that the bottle held less than 500 mL? Explain with an interval.
The cylinder reads to the nearest 2 mL, so the greatest possible error is 1 mL and the volume is from 495 mL to 497 mL. Yes: the whole interval is below 500 mL, so the bottle held 3 to 5 mL less than the label, assuming no water was left in the bottle.
Question 19 of 20 · Short Answer
A school reports that it serves "about 1,200 lunches a day." Last week's counts were 1,184, 1,213, 1,196, 1,227 and 1,179. Is "about 1,200" appropriate, and would "1,199.8 lunches a day" be a better report?
The mean is 5,999 ÷ 5 = 1,199.8 lunches, but daily counts range from 1,179 to 1,227, a spread of 48 lunches. "About 1,200" is appropriate: "1,199.8" suggests a precision that describes no actual day, and a fraction of a lunch has no meaning.
Question 20 of 20 · Short Answer
A cube-shaped box has an edge measured as 20 cm to the nearest centimeter. Its volume is calculated as 8,000 cm³. Find the smallest and largest possible volumes, and compare the percent error of the edge with the percent error of the volume.
Smallest: 19.5³ = 7,414.875 cm³. Largest: 20.5³ = 8,615.125 cm³. The edge is uncertain by 0.5 ÷ 20 = 2.5%, but the volume by about 7.7% upward and 7.3% downward, roughly three times as much, because three uncertain lengths are multiplied. Report about 8,000 cm³, between about 7,400 and 8,600 cm³.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HSN.Q.A.3 mean?
HSN.Q.A.3 means students report quantities with no more and no less accuracy than their measurements support. They find the precision of a tool, treat each reading as an interval, and round results so that every reported digit means something. The standard is about honest reporting, not only about rounding rules.
Is HSN.Q.A.3 the same as significant figures?
Not exactly. Significant-figure rules are one shortcut for choosing how many digits to report, and science courses use them often. HSN.Q.A.3 asks for the reasoning behind them: what the tool can measure and how the error carries into a result. Finding the smallest and largest possible values is a more direct method and works in every case.
What is the difference between precision and accuracy?
Precision describes how finely a tool or a report resolves a quantity; accuracy describes how close a value is to the true value. A stopwatch that shows hundredths is precise, but a hand-timed result can still be inaccurate because of reaction time. Good reports need both, and the number of digits should reflect the real accuracy.
What is the greatest possible error of a measurement?
It is half of the smallest unit the tool reads. A reading to the nearest centimeter is off by at most 0.5 cm, because any true value farther away would have been rounded to a different mark. Adding and subtracting this error from the reading gives the interval of possible true values.
How should students round an answer computed from measurements?
Compute with the full readings, then compute the smallest and largest possible results using the interval ends of each input. Round the answer to the place where the two bounds still agree, or give the range. For a product or quotient, check which combination of inputs gives each bound.
Why is a calculator answer often too precise?
A calculator works with the numbers as if they were exact and shows as many digits as its display holds. It has no way to know that 3.4 m means "somewhere from 3.35 to 3.45 m." Students must decide how many of the digits the measurements support; the calculator cannot.
What mistakes do students make with HSN.Q.A.3?
Common mistakes include copying every calculator digit, treating the full marking interval as the error rather than half of it, and adding a measurement's error directly to an area or volume instead of recomputing with the bounds. Another is rounding so far that real information is lost, such as reporting a careful lab measurement to the nearest ten.
Is HSN.Q.A.3 taught in Algebra 1?
Yes, it is usually taught in Algebra I, often with HSN.Q.A.1 and HSN.Q.A.2 in an opening unit on quantities. It is then used throughout geometry, when students compute areas and volumes from measurements, and in statistics, when they report estimates from samples.
How does HSN.Q.A.3 connect to science labs?
Closely. Lab reports ask students to record measurements to the precision of the instrument and to report calculated results without false precision. The same reasoning about intervals and bounds explains why lab partners get slightly different results and when a difference between two results is large enough to matter.
How can parents help with this standard at home?
Ask how precise a number really is. When a recipe, a news story or a fitness app gives a very exact figure, talk about how it was measured and whether all the digits make sense. Measuring furniture before a move is good practice: the tape reads to a set mark, and a small error in each side matters when the space is tight.
07
Related Standards
6 standards
These standards connect to HSN.Q.A.3: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
5.NBT.A.4Prerequisite
Use place value understanding to round decimals to any place
Lesson coming soon
8.EE.A.4Prerequisite
Operate with scientific notation and choose units of appropriate size
