# Solving for Significant Figures

Hi, I need some assistance with the following questions:

Which of the following has three significant figures?

a. 1.00081 kg

b. 8.060 x 1011 m

c. 0.0500 mm

d. 305.0 cm

(I think the correct answer is d)

Express 0.0015671 to three significant figures.

a. 0.002

b. 0.0016

c. 0.00156

d. 0.00157

(I think the correct answer is a)

#### Solution Preview

Significant figures are a scientist's way of describing how precise a measurement is. When you take a math class, most people don't pay attention to the number of digits a measurement in a problem has. For example, in math 473 and 473.04 are just numbers you use to solve the problem. However, in any physical science, the number of digits reported with the measurement gives you vital information to how good the measuring instrument was. For example, with the 473, the person making the measurement had to "guess" on the three, meaning that there was some uncertainty in the last digit. In contrast with the 473.04, the uncertainty came with the 4 in the hundredths place, making the second measurement much more precise since it could be estimated to a smaller interval. The number of significant figures are the number of measured digits reported. In the first case above, 473 has three significant figures (labelled sf) while 473.04 has 5. The only problem with determining the number of significant figures in a measurement comes when you are dealing with the number zero. Zero is a problem because for many measurements it is necessary to be included so that you have an idea of the ...

#### Solution Summary

This solution provides a very detailed response which clearly explains the topic of significant figures and how to both read and record numbers accurately using this method of notation. This response is about 860 words.