Chapter 3 Mastering Significant Figures and Estimation

What is 4.678 rounded to two significant figures?

• 4.6

• 4.8

• 5.0

• 4.7

Answer explanation

To round 4.678 to two significant figures, look at the first two digits (4.6). The next digit (7) is 5 or more, so round up to 4.7. Thus, the correct answer is 4.7.

Estimate the length of a pencil in centimeters.

• 15 centimeters

• 19 centimeters

• 30 centimeters

• 25 centimeters

Answer explanation

The length of a standard pencil is typically around 19 centimeters, making it the most accurate estimate among the choices provided.

How many significant figures are in the number 0.00456?

• 3

• 5

• 2

• 4

Answer explanation

In the number 0.00456, the leading zeros are not significant. The significant figures are 4, 5, and 6, totaling 3 significant figures. Therefore, the correct answer is 3.

If a recipe calls for 2.5 cups of flour, how would you round this to the nearest whole number?

• 2

• 3

• 2.0

• 4

Answer explanation

To round 2.5 to the nearest whole number, you look at the digit after the decimal. Since it's 5, you round up to 3. Therefore, the correct answer is 3.

Estimate the weight of a textbook in kilograms.

• 3 kg

• 0.5 kg

• 2 kg

• 1.5 kg

Answer explanation

A typical textbook weighs around 1.5 kg, making it a reasonable estimate for an average size and type. The other options, while possible, are either too light or too heavy for standard textbooks.

How many significant figures are in the measurement 1500 m?

• 2

• 1

• 4

• 3

Answer explanation

The measurement 1500 m has 2 significant figures. The trailing zeros are not considered significant unless specified by a decimal point. Therefore, the correct answer is 2.

If you measure a table and find it to be 1.23 m, how would you express this with two significant figures?

• 1.20 m

• 1.23 m

• 1.3 m

• 1.2 m

Answer explanation

To express 1.23 m with two significant figures, we round it to 1.2 m. The first two digits (1 and 2) are significant, while the 3 is not needed for two significant figures.

What is the estimated time it takes to walk 1 mile in minutes?

• 5 to 10 minutes

• 10 to 15 minutes

• 15 to 20 minutes

• 30 to 35 minutes

Answer explanation

The average walking speed is about 3 to 4 miles per hour, which translates to approximately 15 to 20 minutes to walk 1 mile. This makes '15 to 20 minutes' the correct choice for the estimated time.

If a scientist measures a liquid and records it as 3.00 mL, how many significant figures are present?

• 4

• 5

• 3

• 2

Answer explanation

The measurement 3.00 mL has three significant figures. The digits '3', '0', and '0' are all significant, as trailing zeros in a decimal indicate precision.

Round the number 0.00789 to three significant figures.

• 0.0079

• 0.00790

• 0.00788

• 0.00800

Answer explanation

To round 0.00789 to three significant figures, we look at the first three non-zero digits: 789. The next digit (9) rounds the last significant figure (9) up, resulting in 0.00790.