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Chapter 1: Problem 31

How many significant figures are there in each of the following values? a. \(6.07 \times 10^{-15}\) e. \(463.8052\) b. \(0.003840\) f. 300 c. \(17.00\) g. 301 d. \(8 \times 10^{8}\) h. 300 .

Short Answer

Expert verified
The number of significant figures in each value are: a. 3, e. 7, b. 4, f. 1, c. 4, g. 3, d. 1, and h. 3.

Step by step solution

01

a. 6.07 x 10^{-15}

In scientific notation, all digits before the 'x' are considered significant. Therefore, there are 3 significant figures in \(6.07 \times 10^{-15}\).
02

e. 463.8052

All non-zero digits are considered significant.decimal numbers also include significant figures. Therefore, there are 7 significant figures in 463.8052.
03

b. 0.003840

Leading zeros (zeros before the first non-zero digit) are not considered significant but zeros between non-zero digits are considered significant. Here, there are 4 significant figures (3840) after the leading zeros.
04

f. 300

Trailing zeros (zeros after the last non-zero digit) without a decimal point are not considered significant. So there are 1 significant figure in 300.
05

c. 17.00

Trailing zeros after a decimal point are considered significant. Here, we have 2 trailing zeros with a decimal. So there are 4 significant figures in 17.00.
06

g. 301

All non-zero digits are considered significant. Therefore, there are 3 significant figures in 301.
07

d. 8 x 10^8

In scientific notation, all digits before the 'x' are considered significant. Therefore, there is 1 significant figure in \(8 \times 10^8\).
08

h. 300 .

Since there is a decimal point given after '300', it implies that all trailing zeros are considered significant. Thus there are 3 significant figures in 300. In conclusion, the number of significant figures in each of the given values are: a. 3 e. 7 b. 4 f. 1 c. 4 g. 3 d. 1 h. 3

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