Path to Mastering LT 1.4 - Significant Figures

How many significant figures are in the number 0.004560?

• 2

• 3

• 4

• 5

Answer explanation

In the measurement 0.004560, there are 4 significant figures. (The digits that are in blue are significant 0.004560) Leading zeros are never significant and trailing zeros in numbers with a decimal are significant.

Which of the following numbers has three significant figures?

• 0.070

• 0.0070

• 700

• 7.00

Answer explanation

The number 7.00 has three significant figures because the trailing zeros after the decimal point indicate precision. The other options either have fewer significant figures or the leading zeros do not count. Leading zeros are never significant, sandwich zeros are always significant, and trailing zeros in numbers with a decimal are significant.

Round the number 3.1467 to three significant figures.

• 3.14

• 3.15

• 3.146

• 3.147

Answer explanation

To round 3.1467 to three significant figures, look at the fourth digit (6). Since 6 is greater than 5, we round up the third digit (4) to 5, resulting in 3.15.

• 15.3445

• 15.34

• 15.3

• 15.345

Answer explanation

When adding or subtracting, answers must be rounded so the answer has the same number of decimal places as the measurement with the fewest decimal places. The sum of the numbers is 15.3445, but the final answer must be rounded to 1 decimal place (from the measurement 3.2), so it rounds to 15.3.

• 1

• 2

• 3

• 4

Answer explanation

When multiplying and dividing, the answer must be rounded so that it has the same number of significant figures as the measurement with the fewest significant figures. In the calculation 0.0045 × 200.0, the number 0.0045 has 2 significant figures and 200.0 has 4 significant figures. The result should be reported with the least number of significant figures, which is 2.

A student measures the length of a table as 2.345 meters and the width as 1.2 meters. Calculate the area (area = length x width) of the table and express it with the correct number of significant figures.

• 2.814 m²

• 2.81 m²

• 2.8 m²

• 2.8140 m²

Answer explanation

To find the area, multiply length (2.345 m) by width (1.2 m), giving 2.814 m². When multiplying and dividing, the answer must be rounded so that it has the same number of significant figures as the measurement with the fewest significant figures. The width has 2 significant figures, so the area should be expressed with 2 significant figures: 2.8 m² is the correct answer.

How many significant figures are in the measurement 0.02003400?

• 7

• 8

• 5

• 3

Answer explanation

In the measurement 0.02003400, there are 7 significant figures. (The digits that are in blue are significant 0.02003400) Leading zeros are never significant, sandwich zeros are always significant, and trailing zeros in numbers with a decimal are significant.

How many significant figures are in the measurement 202,500 m?

• 4

• 6

• 5

• 3

Answer explanation

In the measurement 202,500, there are 4 significant figures. (The digits that are in blue are significant 202,500) Sandwich zeros are always significant and trailing zeros in numbers with a decimal are significant. Because there is no decimal in this number, the trailing zeros are not significant.

Explain why the number 1000 has only one significant figure, but 1000.0 has five significant figures.

• Because the decimal point in 1000.0 indicates precision.

• Because 1000 is a rounded number.

• Because 1000.0 is a larger number.

• Because 1000.0 is written in scientific notation.

Answer explanation

The number 1000 has only one significant figure because it is considered a rounded number without a decimal point. In contrast, 1000.0 has five significant figures because the decimal point indicates that the measurement is precise.

The rule for trailing zeros is that trailing zeros are significant if there is a decimal anywhere in the number. Trailing zeros are not significant in numbers without a decimal.