Significant Figures and Rounding in Scientific Measurements
Practice reporting measurements with the correct precision
Significant Figures and Rounding in Scientific Measurements
Practice reporting measurements with the correct precision
Science - Grade 9-12
- 1
How many significant figures are in the measurement 0.00450 kg? Explain your answer.
Leading zeros are not significant.
The measurement 0.00450 kg has 3 significant figures. The zeros before 4 are placeholders, but the 4, 5, and final 0 are significant. - 2
For the measurement 700.20 mL, identify which zeros are significant and how many significant figures the measurement has.
The measurement 700.20 mL has 5 significant figures. The two zeros between 7 and 2 are captive zeros, and the final zero after the decimal is also significant. - 3
Round 18.746 m to 3 significant figures.
Keep the first three nonzero or significant digits, then look at the next digit.
18.746 m rounded to 3 significant figures is 18.7 m because the next digit is 4, so the 7 stays the same. - 4
Round 0.00098765 L to 2 significant figures.
0.00098765 L rounded to 2 significant figures is 0.00099 L. The first two significant digits are 9 and 8, and the next digit is 7, so 8 rounds up to 9. - 5
Add the measurements and report the answer with the correct number of decimal places: 12.11 cm + 18.0 cm + 1.013 cm.
For addition and subtraction, round to the least number of decimal places.
The unrounded sum is 31.123 cm. The least precise measurement has 1 decimal place, so the answer should be reported as 31.1 cm. - 6
Multiply and report the answer with the correct number of significant figures: 4.56 m x 1.4 m.
The unrounded product is 6.384 square meters. Since 1.4 has 2 significant figures, the answer should be reported as 6.4 square meters. - 7
A sample has a mass of 15.35 g and a volume of 4.2 mL. Calculate its density and report the answer with the correct number of significant figures.
For multiplication and division, use the least number of significant figures in the measurements.
Density equals mass divided by volume, so 15.35 g divided by 4.2 mL is 3.6547 g/mL. The volume has 2 significant figures, so the density should be reported as 3.7 g/mL. - 8
A graduated cylinder has marks every 1 mL. The bottom of the meniscus is halfway between 36 mL and 37 mL. What volume should be recorded?
Estimate one digit beyond the smallest marked division.
The volume should be recorded as 36.5 mL. Since the cylinder is marked every 1 mL, the measurement should be estimated to the nearest 0.1 mL. - 9
A ruler is marked in millimeters. An object starts at 0.00 cm and ends slightly past 7.3 cm, about 7.34 cm. What measurement should be recorded?
The measurement should be recorded as about 7.34 cm. A ruler marked in millimeters allows measurement to the nearest 0.1 cm and estimation to the nearest 0.01 cm. - 10
Write 6020.0 in scientific notation while preserving all significant figures.
Zeros shown because of a decimal point can be significant.
6020.0 written in scientific notation is 6.0200 x 10^3. This form preserves all 5 significant figures. - 11
A student pours 25.0 mL of water into each of 4 beakers. The number 4 is an exact counted number. What total volume should be reported?
The total volume should be reported as 100.0 mL. The count of 4 beakers is exact, and adding four 25.0 mL measurements gives a total reported to the nearest 0.1 mL. - 12
Convert 3.40 m to centimeters and report the answer with the correct number of significant figures. The conversion 1 m = 100 cm is exact.
Exact conversion factors do not limit the number of significant figures.
3.40 m equals 340 cm. To clearly show 3 significant figures, the answer can be written as 3.40 x 10^2 cm. - 13
Calculate and report the answer with the correct precision: (8.24 g - 1.3 g) divided by 2.0 mL.
Apply the addition or subtraction rule inside the parentheses, then apply the multiplication or division rule.
First subtract: 8.24 g - 1.3 g = 6.94 g, which is limited to 1 decimal place, or 6.9 g. Then divide by 2.0 mL, giving 3.47 g/mL before final rounding. The final answer should be reported as 3.5 g/mL because the division is limited to 2 significant figures. - 14
A digital balance displays a mass of 12.300 g. How many significant figures are shown, and what is the likely precision of the balance?
The mass 12.300 g has 5 significant figures. The balance likely measures to the nearest 0.001 g because the display shows three decimal places. - 15
A cart travels 125.0 m in 9.58 s. Calculate its speed and report the answer with the correct number of significant figures.
A zero after a decimal point can be significant when it shows measured precision.
Speed equals distance divided by time, so 125.0 m divided by 9.58 s is 13.048 m/s. Since 9.58 has 3 significant figures, the speed should be reported as 13.0 m/s.