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Chapter 1: Problem 20

How many significant figures are shown in each of the following? If this is indeterminate, explain why. (a) 450 ; (b) 98.6 ; (c) $0.0033 ; (d) 902.10 ; (e) 0.02173 ; (f) 7000 ; (g) 7.02 ; (h) 67,000,000

Short Answer

Expert verified
(a) 2; (b) 3; (c) 2; (d) 5; (e) 3; (f) Indeterminate; (g) 3; (h) Indeterminate.

Step by step solution

01

Determine Significant Figures for (a) 450

There are two non-zero digits (4 and 5) and a trailing zero at the end without a decimal point. According to the rules, the trailing zero in this case is ambiguous or indeterminate. So, the number of significant figures is 2.
02

Determine Significant Figures for (b) 98.6

There are three digits including two non-zero digits (9 and 8) and one zero digit after the decimal point. According to the rules, the zero after the decimal point is considered significant. So, the number of significant figures is 3.
03

Determine Significant Figures for (c) 0.0033

There are four digits in total including two significant non-zero digits (3 and 3) and two leading zeroes. According to the rules, leading zeroes are not significant. So, the number of significant figures is 2.
04

Determine Significant Figures for (d) 902.10

This number has five digits included, two zero digits and three non-zero digits (9, 2, and 1). According to the rules, zeroes between non-zero digits and trailing zero after a decimal point are considered significant. So, the number of significant figures is 5.
05

Determine Significant Figures for (e) 0.02173

The number has five digits including two leading zeroes, which are not significant, and three non-zero digits (2, 1, and 3). So, the number of significant figures is 3.
06

Determine Significant Figures for (f) 7000

There is one non-zero digit (7) and three trailing zeroes without a decimal point, which are ambiguous or indeterminate. Therefore, the number of significant figures is indeterminate; it can be 1 or 4 depending on whether or not those zeroes are intended to be significant.
07

Determine Significant Figures for (g) 7.02

The number has one zero digit between two non-zero digits (7 and 2). According to the rules, zeroes between significant digits are considered significant. So, the number of significant figures is 3.
08

Determine Significant Figures for (h) 67,000,000

This number has two non-zero digits (6 and 7) and six trailing zeros after these digits without a decimal point, which are ambiguous or indefinite. So, the number of significant figures is indeterminate; it can be 2 or 8 depending on whether or not those zeroes are intended to be significant.

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Most popular questions from this chapter

The highest temperature of the following group is (a) \(217 \mathrm{K} ;\) (b) \(273 \mathrm{K} ;\) (c) \(217^{\circ} \mathrm{F} ;\) (d) \(105^{\circ} \mathrm{C} ;\) (e) \(373 \mathrm{K}\).

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