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Chapter 1: Problem 34

How many significant figures are in each of the following? a. 100 b. \(1.0 \times 10^{2}\) c. \(1.00 \times 10^{3}\) d. 100 e. 0.0048 f. 0.00480 g. \(4.80 \times 10^{-3}\) h. \(4.800 \times 10^{-3}\)

Short Answer

Expert verified
a. 1 significant figure b. 2 significant figures c. 3 significant figures d. 1 significant figure e. 2 significant figures f. 3 significant figures g. 3 significant figures h. 4 significant figures

Step by step solution

01

a. 100

Here, there are no decimal points and trailing zeros. Thus, we only count the non-zero digit. The number of significant figures is 1.
02

b. \(1.0 \times 10^{2}\)

In scientific notation, all the digits before the multiplication sign are considered significant. Here, there are two significant digits - 1 and 0. So, the number of significant figures is 2.
03

c. \(1.00 \times 10^{3}\)

Like in the previous example, all the digits before the multiplication sign are significant. Here, we have three significant digits - 1, 0, and 0. So, there are 3 significant figures.
04

d. 100

Here, there are no decimal points and trailing zeros. Thus, we only count the non-zero digit. The number of significant figures is 1.
05

e. 0.0048

In this case, leading zeros are not significant. Therefore, we only count the non-zero digits. There are 2 significant figures in this number.
06

f. 0.00480

In this case, the trailing zero appears after a decimal point, which means it is significant. Along with the non-zero digits, we have a total of 3 significant figures.
07

g. \(4.80 \times 10^{-3}\)

In scientific notation, all the digits before the multiplication sign are considered significant. Here, there are three significant digits - 4, 8, and 0. So, the number of significant figures is 3.
08

h. \(4.800 \times 10^{-3}\)

Similar to the previous example, all digits before the multiplication sign are significant. Here, we have four significant digits - 4, 8, 0, and 0. Thus, there are 4 significant figures.

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