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Chapter 1: Problem 19

Express each of the following to fur significant figures. (a) 3984.6 (b) 422.04 (c) 0.0033 (d) 902.10 (e) 0.02173 (f) 7000 (g) 7.02 (h) 67,000,000

Short Answer

Expert verified
The numbers expressed to four significant figures are: (a) 3985, (b) 422.0, (c) 0.0033, (d) 902.1, (e) 0.02173, (f) 7000, (g) 7.02, (h) 67,000,000.

Step by step solution

01

Identify the significant figures of 3984.6

All non-zero numbers are considered significant. So, 3984.6 has five significant figures. To express this as four significant figures, round it off. Using rounding rules, 3984.6 becomes 3985.
02

Identify the significant figures of 422.04

All non-zero numbers are considered significant. So, 422.04 also has five significant figures. To express this as four significant figures, round it off. Using rounding rules, 422.04 becomes 422.0.
03

Identify the significant figures of 0.0033

Leading zeros are not significant, they're just placeholders. Therefore, 0.0033 has two significant figures. No adjustment is necessary here because it already has less than four significant figures.
04

Identify the significant figures of 902.10

The zero in 902.10 is significant because it is a trapped zero (between nonzero digits). Therefore, 902.10 has five significant figures. To get four significant figures, this needs to be rounded off. Applying rounding rules, 902.10 becomes 902.1.
05

Identify the significant figures of 0.02173

The zeros in the front are placeholders while the zero after 7 is a significant figure, so 0.02173 has four significant figures. No adjustment is necessary here because it already has four significant figures.
06

Identify the significant figures of 7000

In the number 7000, without a decimal point, the trailing zeros are not significant. They are considered placeholders. So, 7000 only has one significant figure, which is 7. Therefore, no adjustment is necessary here because it's already in less than four digits.
07

Identify the significant figures of 7.02

In the number 7.02, both digits and the decimal point are significant, leading to three significant figures. No adjustment is required because it already has less than four significant figures.
08

Identify the significant figures of 67,000,000

In the number 67,000,000, the trailing zeros are not considered significant without a decimal point. Hence, there are only two significant figures in this number. There is no need to reduce it to four significant figures, as it already has fewer than four.

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