Q. 2.82 - An Introduction to General, Organic, and Biological Chemistry

Question

In which of the following pairs do both numbers contain the same number of significant figures? $(2.2)$

a. $3.44\times {10}^{-1}\mathrm{g} and 0.0344 \mathrm{g}$

b. $0.0098 \mathrm{s} and 9.8\times {10}^4 \mathrm{s}$

c. $6.8\times {10}^3 \mathrm{m} and 68000 \mathrm{m}$

d. $2.58 .000 \mathrm{g} and 2.58\times {10}^{-2} \mathrm{g}$

Step-by-Step Solution

Answer

Part (a) As a result, the number of significant figures in both numbers is the same.

Part (b) As a result, they both have the same amount of significant figures.

Part (c)  As a result, the number of significant figures in both bullet numbers is the same.

Part (d) As a result, neither number has the same amount of significant figures.

Part (a) Step 1 : Introduction

The given is the pair of numbers contains same numbers and significant figures

The objective is to determine which is the pair of numbers with same number and significant figures

Part (a) Step 2 : Explanation

a. 

Because all nonzero digits are significant, the quantity $3.44\times {10}^{-3} \mathrm{g}$ has three significant figures. The major figures are unaffected by the exponential term.

Because all nonzero digits are important and zeros to the left of the first nonzero digit are not significant; they simply serve to locate the decimal point, the quantity $0.0344 \mathrm{m}$ contains three significant figures. As a result, the number of significant figures in both numbers is the same.

Part (b) Step 3 : Introduction

The objective is to determine which is the pair of numbers with same number and significant figures

Part (b) Step 4 : Explanation

b.

Because all nonzero digits are significant and zeros to the left of the first nonzero digit are not significant, the amount$0.0098 \mathrm{S}$ has two significant figures. Because all nonzero digits are significant, the amount $9.8 \times {10}^4 \mathrm{S}$contains two significant figures. As a result, the number of significant figures in both numbers is the same,

Part (c) Step 5 : Introduction

The objective is to determine which is the pair of numbers with same number and significant figures

Part (c) Step 6 : Explanation

C.

Because all nonzero digits are significant, the amount $9.4 \times {10}^{4 } \mathrm{m}$ contains two significant figures. Because all nonzero digits are significant and zeros at the end of a number are significant if the number has a decimal point, the quantity $68,000 \mathrm{m}$ has two significant figures.

As a result, the number of significant figures in both numbers is the same.

Part (d) Step 7 : Introduction

The objective is to determine which is the pair of numbers with same number and significant figures

Part (d) Step 8 : Explanation

d) 

Because all nonzero digits are significant and zeros at the end of a number are significant if the number has a decimal point, the quantity$258.000$ has $6$ significant figures. Because all nonzero digits are significant, the amount $2.58\times {10}^{-2} \mathrm{g}$ has three significant figures. The major figures are unaffected by the exponential term. As a result, neither number has the same amount of significant figures.