Q. 2.12 - 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?

a. $0.00575 and 5.75\times {10}^{-3}$

b. $405 k and 405.0 K$

c. $150000 s and 1.50\times {10}^4$s

d.  $3.8\times {10}^{-2} L and 3.0\times {10}^{5}L$

Step-by-Step Solution

Answer

Part a and part d both contain the same number of significant figures.

Part (a) step 1: Given Information

We need to find whether both the numbers in each pair contain the same number of significant figures or not. 

Part (a) step 2: Explanation

Referring to the rules in the significant figure as summarized by the table : $2.2$

The number $0.00575$ has three significant figures-three non-zero digits, and the zeroes are just placeholders. The other number $5.75\times {10}^{-3}$ has three significant figures-the coefficient of this number is 5.75 which means it has 3 sig figs and the zeroes are non-significant. Therefore, the two numbers in the pair  have the same numbers of significant figures.

Part (b) step 1: Given Information

We need to find whether both the numbers in each pair contain the same number of significant figures or not 

Part (b) step 2: Explanation

Referring to the rules in the significant figure as summarized by the table: $2.2$

The number $405 k$has three significant figures-the non-zero digits and the zero at the middle. The other number $405.0 K$ have also four significant figures-the non-zero digits and the two zeros, one at the middle and the other at the end. Therefore, the  two numbers in this pair do not have the same number of significant figures.

Part (c) step 1: Given Information

We need to find whether both the numbers in each pair contain the same number of significant figures or not 

Part (c) step 2: Explanation

Referring to the rules in the significant figure as summarized by the table: $2.2$

The number $15000$ have two significant figures-the two non-zero digits (1 and 5) and all the other zeros are placeholders. The other number$1.50\times {10}^4$ have three significant figures-the non-zero digits and the zero at the end (1,5 and 0). Therefore, two numbers in this pair do not have the same number of significant figures-.

Part (d) step 1: Given Information

We need to find whether both the numbers in each pair contain the same number of significant figures or not 

Part (d) step 2: Explanation

Referring to the rules in the significant figure as summarized by the table: $2.2$

There is the same number of significant digits in both the numbers; two. On the first number, both non-zero digits are significant (3 & 8). On the second number, the non-zero and the zero digits are significant (3 & 0). Therefore, the two numbers in this pair have the same number of significant figures.