Q. 2.13 - An Introduction to General, Organic, and Biological Chemistry

Question

Indicate if the zeros are significant in each of the following measurements: 

a. $0.0038m$                  b. $5.04 cm$

c. $800 L$                        d. $3.0\times {10}^{-3} kg$

e. $85 000g$

Step-by-Step Solution

Answer

a. In $0.0038 m$ there are two significant figures which are $3$ and $8$.

b. In $5.04 cm$ there are three significant figures which are $5, 0 and 4$.

c. In $800 L$ there are three significant figures which are $8$ and two non-zero digits.

d. In $3.0\times {10}^{-3} kg$ there are two significant figures which are $3 \mathrm{and} 0$.

e. In $85 000 g$ there are two significant figures which are $8 \mathrm{and} 5$.

Part (a) Step 1: Given Information

We need to find the number of significant figures in $0.0038 m$.

Part (a) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

Table Significant figures in measured numbers

There are two significant figures, the non-zero digits $3$ and $8$, since the rest digits are the placeholders.

Part (b) Step 1: Given Information

We need to find the number of significant figures in $5.04 cm$.

Part (b) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

Table Significant figures in measured numbers

There are three significant figures, that is $5, 0 and 4$.

Part (c) Step 1: Given Information

We need to find the number of significant figures in $800 L$.

Part (c) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

Table Significant figures in measured numbers

There are three significant figures, the non-zero digit $8$ and the two zeros which denote the uncertainty at one digit.

Part (d) Step 1: Given Information

We need to find the number of significant figures in $3.0\times {10}^{-3}kg$.

Part (d) Step 1: Explanation

Considering the rules in significant figures as summarized by the table is

Table Significant figures in measured numbers

There are two significant figures, the non-zero digit $3$ and one zero which denotes the uncertainty at the $10th$digit.

Part (e) Step 1: Given Information

We need to find the number of significant figures in $85 000g$.

Part (e) Step 2: Explanation

Considering the rules in significant figures as summarized by the table is

Table Significant figures in measured numbers

There are two significant figures, the non-zero digits $8$ and $5$, and the remaining digits are just placeholders.