Significant figures practice gets easier when you separate two decisions: which digits belong to a measurement, and which rounding rule belongs to a calculation. For addition and subtraction, track the last reliable place. For multiplication and division, track the number of significant figures. Keep extra calculator digits during the work, then report the final answer with the appropriate precision.
The exercises below cover zeros, scientific notation, exact numbers, and calculations that mix operations. Each answer explains the decision that controls the result. All measurements and lab situations are invented for practice. Unless an exercise says otherwise, treat the supplied values as measurements, not exact counts.
A short rule sheet before you begin
Nonzero digits count. Zeros between significant digits count. Leading zeros locate the decimal point and don’t count. Trailing zeros after a decimal point do count. A whole number such as 700 can be ambiguous without context; scientific notation makes the intended precision clear.
For multiplication or division, use the fewest significant figures among the measured inputs. For addition or subtraction, use the least precise place among them. Exact counts and defined conversion factors don’t limit precision. These are introductory reporting conventions, not a replacement for a formal uncertainty analysis. See OpenStax’s measurement and significant-figure guidance for the underlying rules.
Before touching your calculator, put a box around the requested unit and underline the input that will limit the answer. If you can’t identify that input yet, leave a question mark beside it. That small pause makes your reasoning visible when you check the exercise.
Part 1: Count the significant figures
1. A small mass: 0.004080 g
Question: How many significant figures does this measurement contain?
Answer: four. The zeros before 4 only locate the decimal point. Start counting at 4: the digits are 4, 0, 8, and the final 0. The middle zero counts because it sits between significant digits. The last zero counts because it follows the decimal point and a nonzero digit.
A useful rewrite is 4.080 x 10-3 g. The coefficient displays all four significant figures without the distracting leading zeros. Don’t change it to 4.08 if the question asks you to preserve the original precision.
2. Three versions of the same numerical value
Question: Compare 6 x 102 mL, 6.0 x 102 mL, and 6.00 x 102 mL.
Answer: one, two, and three significant figures. Each expression represents a numerical value of 600 mL, but the written measurements communicate different precision. Count digits in the coefficient, not in the exponent.
If a worksheet gives only 600 mL, check its stated convention or measurement context. Don’t silently add a decimal point to force an answer. On your own notes, scientific notation is a clearer way to distinguish a value reported to the hundreds place from one reported to the tens or ones place.
3. An exact count beside a measurement
Question: You count exactly 12 identical sample containers. Their combined measured mass is 48.36 g. What is the mean mass per container?
Answer: 4.030 g. Calculate 48.36 g divided by 12 containers. The count is exact, so its two written digits don’t limit the result to two significant figures. The four significant figures in the measured mass control the reported mean.
This exercise asks for an arithmetic mean. It doesn’t establish that every individual container weighs exactly 4.030 g. Keep that distinction in mind when a lab question asks about variation among objects rather than their average.
Part 2: Choose the rule before rounding
4. Add measured masses
Question: Report 12.11 g + 0.3 g + 1.024 g with appropriate precision.
Answer: 13.4 g. The calculator sum is 13.434 g. The least precise measurement, 0.3 g, is reported to the tenths place. Round the sum to that place.
A tempting wrong answer is 10 g, obtained by noticing that 0.3 has one significant figure and applying the multiplication rule. But this problem contains addition. Your limiting label should say tenths place, not one significant figure. Write those labels in words until you stop mixing them up.
5. Subtract two volume readings
Question: A cylinder reading changes from 18.24 mL to 25.6 mL. Find the change in volume.
Answer: 7.4 mL. The unrounded difference is 7.36 mL. The final reading is given to the tenths place, so the difference is reported to the tenths place as well.
The answer has two significant figures even though the input values have three and four. That’s fine. Subtraction follows place precision, and subtracting nearby numbers can leave a result with fewer significant figures. Don’t add a zero merely to make the digit count resemble the inputs.
6. Multiply two lengths
Question: A rectangular label measures 3.24 cm by 2.1 cm. Calculate its area.
Answer: 6.8 cm2. Multiplication gives 6.804 cm2. The lengths have three and two significant figures, so report two. Keep 6 and 8, then inspect the next digit, 0. No increase is needed.
The unit also changes: length multiplied by length gives area. A numerically correct answer labeled cm would still be incomplete. If units are the difficult part, use the separate dimensional-analysis practice problems before combining conversion and precision decisions.
7. Divide mass by volume
Question: A fictional liquid sample has a mass of 18.42 g and a volume of 6.0 mL. Calculate its density.
Answer: 3.1 g/mL. The quotient is 3.07 g/mL. The volume has two significant figures, so keep two in the result. The third digit is 7, which rounds 3.0 upward to 3.1.
Don’t report 3.07 just because the calculator stops there. Calculator output describes the arithmetic performed on the entered numbers. It doesn’t know the measurement precision that your lab report needs to communicate.
Part 3: Track precision through mixed operations
8. Find a sample mass, then calculate density
Question: A container and sample together weigh 15.67 g. The empty container weighs 12.3 g. The sample volume is 2.40 mL. Calculate density.
First subtract: 15.67 − 12.3 = 3.37 g. The subtraction step supports the tenths place, equivalent here to two significant figures in the sample mass. Record that limitation, but keep 3.37 in your calculator.
Then divide: 3.37 / 2.40 = 1.404166… g/mL. The sample mass limits the final quotient to two significant figures. Report 1.4 g/mL. The extra digits were carried for arithmetic; they weren’t a claim of extra measurement precision.
Set up a two-line precision record in your notes: mass difference, tenths place; density quotient, two significant figures. Writing that record is more reliable than applying the fewest digit count from the original inputs to the entire expression without considering its operations.
9. Catch a premature-rounding error
Question: Evaluate (1.26 + 1.27) / 1.3 using the usual introductory rules.
The sum is 2.53, supported to the hundredths place. Division by 1.3 limits the final answer to two significant figures. Keep the full sum: 2.53 / 1.3 = 1.946153… . The answer is 1.9.
If you prematurely round the sum to 2.5 because you notice the denominator has two significant figures, the quotient becomes 1.923076… . It happens to round to the same answer here, but the intermediate arithmetic has changed unnecessarily. Matching the answer key doesn’t make that shortcut dependable. Preserve the sum and apply the limitation at the correct step.
10. Distinguish the rounding place from the digit count
Question: Add 5 x 102 g and 1.365 g. The first value is explicitly a measurement reported to the hundreds place.
Answer: 5 x 102 g. The arithmetic sum is 501.365 g, but the hundreds place limits the reported sum. Reporting 501 g would imply a ones-place precision that the first measurement doesn’t provide.
This is why the shorthand “fewest decimal places” can mislead you with whole numbers. The relevant place can lie to the left of the decimal point. Write the place as hundreds, tens, ones, tenths, or hundredths instead of assuming every whole number is known to the ones place.
Use your mistakes to build a useful review sheet
Cover the answers and redo three exercises on a blank page: one counting problem, one single-operation calculation, and one mixed-operation calculation. For every miss, write the exact decision you changed. Examples include “counted leading zeros,” “used significant-figure count for addition,” and “forgot that 12 was an exact count.”
Keep the question, your first setup, and the corrected explanation together. A page of final answers alone won’t show why you chose a rule. You can compare your course terminology with the materials on StudyUpload’s Chemistry subject page or browse shared study documents.
When you’ve made a clear original practice sheet, upload your own notes to help other students. Include measurement assumptions and worked reasoning, and share only material you’re allowed to distribute.
Frequently asked questions
Does 0.0500 have two or three significant figures?
Three: 5 and the two following zeros. The initial zeros locate the decimal point. Writing 5.00 x 10-2 makes the count easier to see.
Should I round every intermediate answer?
Usually, carry extra digits and round the final answer. Still record the precision limitation at each operation. If a worksheet requests an intermediate reported value, show that rounded value while retaining extra digits for later arithmetic.
What happens when the discarded digit is exactly 5?
Courses can specify different tie conventions, including rounding to even. Follow the convention given for your class. None of the rounding exercises here depends on an exact halfway tie.
Do defined unit conversions reduce significant figures?
No. An exact definition, such as 100 centimeters per meter, doesn’t impose a digit limit. A measured conversion relationship, such as a sample’s measured density, can impose one. Identify which type you have before counting digits.