Q. 2.9 - An Introduction to General, Organic, and Biological Chemistry

Question

How many significant figures are in each of the following?

 a. $11.005 \text{g}$
 b. $0.00032 \text{m}$
 c. $36000000 \text{km}$
 d. $1.80\times {10}^4 \text{kg}$
 e. $0.8250 \text{L}$
 f. ${30.0}^{\circ } \text{C}$

Step-by-Step Solution

Answer

a. There are five significant figures in $11.005 \text{g}$.

b. There are two significant figures in   $0.00032 \text{m}$.

c. There are two significant figures in $36000000 \text{km}$.

d. There are three significant figures in $1.80\times {10}^4 \text{kg}$.

e. There are four significant figures in $0.8250 \text{L}$

f. There are three significant figures in  ${30.0}^{\circ } \text{C}$.

Part (a) step 1: Given Information

We need to find the number of significant figures in $11.005 \text{g}$.

Part (a) step 2: Explanation

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

Table $2.2$ Significant Figures in Measured Numbers

Now, there would be five significant figures-  the three nonzero digits and the two zeroes in between.

Part (b) step 1: Given Information

We need to find the number of significant figures in $0.00032 \text{m}$. 

Part (b) step 2: Explanation

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

Table $2.2$ Significant Figures in Measured Numbers

Now, there would be two significant figures-  the nonzero digits $2$and  $3$the rest are just placeholders and are thus insignificant.

Part (c) step 1: Given Information

We need to find the number of significant figures in $36000000 \text{km}$.

Part (c) step 2: Explanation

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

Table $2.2$  Significant Figures in Measured Numbers

Now, there would be two significant figures-  the nonzero digits $3$ and $6$ the rest are just placeholders and are thus insignificant.

Part (d) step 1: Given Information

We need to find the number of significant figures in $1.80\times {10}^4 \text{kg}$.

Part (d) step 2: Explanation

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

Table $2.2$ Significant Figures in Measured Numbers

Now, there would be three significant figures-  the nonzero digits $1$ and $8$ , and the zeroes in the end.

Part (e) step 1: Given Information

We need to find the number of significant figures in $0.8250 \text{L}$.

Part (e) step 2: Explanation

Referring to the rules in the significant figure as summarized by the table:$2.2$
Table $2.2$ Significant Figures in Measured Numbers

Now, there would be four significant figures-  the nonzero digits, and zero at the end. The zero before the nonzero digits are more placeholders and, therefore are thus not significant.

Part (f) step 1: Given Information

We need to find the number of significant figures in  ${30.0}^{\circ } \text{C}$.

Part (f) step 2: Explanation

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

Table $2.2$  Significant Figures in Measured Numbers

Now, there would be three significant figures-  the nonzero digits $3$, and the two zeroes in the end.