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Chapter 1: Problem 30

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. 3 significant figures e. 2 significant figures f. 3 significant figures g. 3 significant figures h. 4 significant figures

Step by step solution

01

a. 100

This number has trailing zeros with no decimal point, so the trailing zeros do not count as significant. Thus, there is only 1 significant digit: "1".
02

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

There is a non-zero digit (1) and a trailing zero with a decimal point (0), making 2 significant figures: "1.0".
03

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

There is a non-zero digit (1) and two trailing zeros with decimal points (0, 0), making 3 significant figures: "1.00".
04

d. 100 .

This number has trailing zeros and a decimal point, which makes the trailing zeros significant. There are 3 significant digits: "100".
05

e. 0.0048

There are leading zeros, which are not significant, and two non-zero digits (4, 8). There are 2 significant figures: "4.8".
06

f. 0.00480

There are leading zeros, which are not significant, and two non-zero digits (4, 8) followed by a trailing zero with a decimal point (0). There are 3 significant figures: "4.80".
07

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

There are two non-zero digits (4, 8), and a trailing zero with a decimal point (0). There are 3 significant figures: "4.80".
08

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

There are two non-zero digits (4, 8), and two trailing zeros with decimal points (0, 0). There are 4 significant figures: "4.800".

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