Significant Figures and Rounding in Scientific Measurements Worksheet

Question 1

How many significant figures are in the measurement 0.00450 kg? Explain your answer.

Accepted Answer

The measurement 0.00450 kg has 3 significant figures. The zeros before 4 are placeholders, but the 4, 5, and final 0 are significant.

Question 2

For the measurement 700.20 mL, identify which zeros are significant and how many significant figures the measurement has.

Accepted Answer

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.

Question 3

Round 18.746 m to 3 significant figures.

Accepted Answer

18.746 m rounded to 3 significant figures is 18.7 m because the next digit is 4, so the 7 stays the same.

Question 4

Round 0.00098765 L to 2 significant figures.

Accepted Answer

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.

Question 5

Add the measurements and report the answer with the correct number of decimal places: 12.11 cm + 18.0 cm + 1.013 cm.

Accepted Answer

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.

Question 6

Multiply and report the answer with the correct number of significant figures: 4.56 m x 1.4 m.

Accepted Answer

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.

Question 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.

Accepted Answer

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.

Question 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?

Accepted Answer

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.

Question 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?

Accepted Answer

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.

Question 10

Write 6020.0 in scientific notation while preserving all significant figures.

Accepted Answer

6020.0 written in scientific notation is 6.0200 x 10^3. This form preserves all 5 significant figures.

Question 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?

Accepted Answer

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.

Question 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.

Accepted Answer

3.40 m equals 340 cm. To clearly show 3 significant figures, the answer can be written as 3.40 x 10^2 cm.

Question 13

Calculate and report the answer with the correct precision: (8.24 g - 1.3 g) divided by 2.0 mL.

Accepted Answer

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.

Question 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?

Accepted Answer

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.

Question 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.

Accepted Answer

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.

Significant Figures and Rounding in Scientific Measurements

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