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Chapter 1: Problem 33

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

Short Answer

Expert verified
a. 3 significant figures b. 4 significant figures c. 4 significant figures d. 1 significant figure e. 7 significant figures f. 1 (or 3) significant figure(s) g. 3 significant figures h. 1 (or 3) significant figure(s)

Step by step solution

01

(Step 1: Identifying significant figures in a number in scientific notation)

For values in scientific notation, count all nonzero digits and also the trailing zeroes. These digits are significant because they contribute to the precision of the number. a. \(6.07 \times 10^{-15}\) There are 3 significant figures: 6 (nonzero digit), 0 (trailing zero), and 7 (nonzero digit).
02

(Step 2: Identifying significant figures in a number with leading zeroes)

Do not count leading zeroes as significant figures. Leading zeroes serve only to position the decimal point and do not contribute to the precision of the number. b. 0.003840 There are 4 significant figures: 3 (nonzero digit), 8 (nonzero digit), 4 (nonzero digit), and 0 (trailing zero).
03

(Step 3: Identifying significant figures in a number with decimal point and trailing zeroes)

Trailing zeroes in a number with a decimal point are significant figures because they indicate the level of precision. c. 17.00 There are 4 significant figures: 1 (nonzero digit), 7 (nonzero digit), 0 (trailing zero), and 0 (trailing zero).
04

(Step 4: Identifying significant figures in a number in scientific notation with no trailing zeroes)

For values in scientific notation with no trailing zeroes, count all nonzero digits as significant figures. d. \(8 \times 10^8\) There is 1 significant figure: 8 (nonzero digit).
05

(Step 5: Identifying significant figures in a number with nonzero digits and trailing zeroes)

Trailing zeroes after a nonzero digit and before a decimal point are not always significant figures. Unless otherwise specified, assume that trailing zeroes in a whole number without a decimal point are not significant. e. 463.8052 There are 7 significant figures: 4 (nonzero digit), 6 (nonzero digit), 3 (nonzero digit), 8 (nonzero digit), 0 (trailing zero), 5 (nonzero digit), and 2 (nonzero digit). f. 300 There is 1 significant figure (or 3, depending on context and if the zeroes are explicitly stated as significant): 3 (nonzero digit).
06

(Step 6: Identifying significant figures in a number with trailing zeroes)

Trailing zeroes after a nonzero digit and before a decimal point are not significant figures unless otherwise specified or if the number is in scientific notation. In these cases, count the trailing zeroes as significant. g. 301 There are 3 significant figures: 3 (nonzero digit), 0 (zero between nonzero digits), and 1 (nonzero digit). h. 300 There is 1 significant figure (or 3, depending on context and if the zeroes are explicitly stated as significant): 3 (nonzero digit).

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