FULL REVIEW
Full Review — Significant Figures and Measurement Uncertainty — Algebra-Based
Review the essential ideas, relationships, and problem-solving tools for Significant Figures and Measurement Uncertainty.
TIME
45–60 minutes
BEST FOR
A complete topic review
FINISH WITH
A readiness check
After this full review, you'll be able to...
recall the essential ideas, apply them to representative problems, and determine what to study next.
Choose how you want to review
Course Alignment
This Physics Sensei Topic Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
Related Unit Review: If you need to review the complete unit material, review Units and Measurements here →
RESOURCE: Physics Sensei Topic Review | TOPIC ID: MEC-U01-T02 | TOPIC: Significant Figures and Measurement Uncertainty | PARENT UNIT: MEC-U01 — Units and Measurements | COURSE LEVEL: Algebra-Based College Physics
BEST USED ✓ After learning the topic ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 45–60 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Recall Activity 1
Answer before revealing the response.
How many significant figures are in 6.020 × 10³?
Reveal Answers
6.020 × 10³ has four significant figures.
Why it works: Scientific notation makes the intended significant digits explicit.
ACTIVITY 2
Recall Activity 2
Answer before revealing the response.
A result is 18.7426 cm from a calculation, but the inputs justify only three significant figures. How should it be reported?
Reveal Answers
Report 18.7 cm.
Why it works: Three significant figures retain only the digits justified by the input precision.
ACTIVITY 3
Recall Activity 3
Answer before revealing the response.
A voltage is 12.0 ± 0.3 V. Estimate its percent uncertainty.
Reveal Answers
About 2.5%.
Why it works: Relative uncertainty compares the uncertainty magnitude with the measured value.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
Rounding Rules for Calculated Results
For multiplication and division, the result is usually limited by the input with the fewest significant figures. For addition and subtraction, the limiting factor is decimal place rather than a raw count of significant figures. Keep extra digits during intermediate steps and round once at the end.
Multiplication/division: final significant figures follow the least-precise factor
Example: (3.42)(2.1) = 7.182 on the calculator, reported as 7.2 because 2.1 has two significant figures.
Sensei note: Do not round every intermediate line; repeated rounding can shift the final answer.
KEY CONCEPT 2
Absolute and Percent Uncertainty
Absolute uncertainty has the same units as the measured quantity. Percent uncertainty expresses that uncertainty relative to the size of the measurement, making it easier to compare measurements of different magnitudes.
Percent uncertainty = (absolute uncertainty / measured value) × 100%
Example: For 80.0 ± 2.0 N, the percent uncertainty is 2.5%.
Sensei note: A small absolute uncertainty can still be large in percentage terms if the measured value is small.
KEY CONCEPT 3
Combining Uncertainty in Simple Calculations
For simple introductory estimates, absolute uncertainties are often tracked for sums/differences and relative or percent uncertainties for products/quotients. The exact method depends on the stated uncertainty model, so identify the convention being used before calculating.
Products/quotients: compare or combine relative uncertainties
Example: If two measured factors each have a few percent uncertainty, the result cannot reasonably be reported to many more precise digits than those inputs support.
Sensei note: State the propagation convention; different laboratory courses may use worst-case or independent-random rules.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Round a Product
Worked Example
Calculate (4.62 m)(3.1 m) and report the area with appropriate significant figures.
Reveal Answers
The calculator gives 14.322 m². The factor 3.1 has two significant figures, so report 14 m².
Why it works: The solution applies the stated precision or uncertainty method while keeping the final report consistent with the data.
PRACTICE 2
Compare Relative Precision
Guided Problem
Measurement A is 20.0 ± 0.2 cm. Measurement B is 5.0 ± 0.2 cm. Which has better relative precision?
Reveal Answers
A has 1% uncertainty; B has 4% uncertainty. Measurement A has better relative precision.
Why it works: The solution applies the stated precision or uncertainty method while keeping the final report consistent with the data.
PRACTICE 3
Report a Quotient
Independent Problem
A distance 24.0 ± 0.2 m is divided by a time 3.00 ± 0.05 s. Estimate the speed and judge a sensible number of reported digits.
Reveal Answers
The speed is 8.00 m/s. The relative uncertainties are under 2%, so a report around 8.00 m/s with an uncertainty on the order of tenths is sensible; use the course-specified propagation rule for the exact uncertainty.
Why it works: The solution applies the stated precision or uncertainty method while keeping the final report consistent with the data.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Decimal-Place Rule
Apply the addition/subtraction rule.
Report 12.43 + 1.2 + 0.056 with appropriate decimal precision.
Reveal Answers
The calculator gives 13.686; the least precise term is to the tenths place, so report 13.7.
Why it works: The answer follows directly from the measurement-precision or propagation principle tested by the question.
QUICK CHECK 2
Percent Uncertainty
Compute the relative precision.
A mass is 125.0 ± 0.5 g. What is the percent uncertainty?
Reveal Answers
0.4%.
Why it works: The answer follows directly from the measurement-precision or propagation principle tested by the question.
QUICK CHECK 3
Guard Digits
Choose a calculation strategy.
Should you round intermediate values after every line or retain extra digits until the final result?
Reveal Answers
Retain extra digits and round the final reported result.
Why it works: The answer follows directly from the measurement-precision or propagation principle tested by the question.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
Round by the Operation
Multiplication/division uses significant-figure limits; addition/subtraction uses decimal-place limits.
KEY TAKEAWAY 2
Use Relative Uncertainty
Percent uncertainty compares measurement quality on a common scale and helps determine sensible reporting precision.
KEY TAKEAWAY 3
Propagation Comes Before Final Rounding
Estimate the uncertainty or limiting precision first, then round the final value to match it.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
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