Q. 2.10 - An Introduction to General, Organic, and Biological Chemistry

Question

How many significant figures are in each of the following?

 a.  $20.60 \text{mL}$
 b.  $1036.48 \text{kg}$
 c.  $4.00 \text{m}$
 d.  ${20.8}^{\circ }\text{C}$
 e.  $60800000 \text{g}$
 f. $5.0\times {10}^{-3} \text{L}$

Step-by-Step Solution

Answer

a.  There are four significant figure is $20.60 \text{mL}$.

b.  There are six significant figure is$1036.48 \text{kg}$.

c.  There are three significant figure is $4.00 \text{m}$.

d.  There are three significant figure is${20.8}^{\circ } \text{C}$.

e.  There are three significant figure is$60800000 \text{g}$.

f.  There are three significant figure  is$5.0\times {10}^{-3} \text{L}$.

Part (a) step 1: Given Information

We need to find the number of significant figures $20.60 \text{mL}$.

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 four significant figures-  the two nonzero digits, and zero at the middle and at the end.

Part (b) step 1: Given Information

We need to find the number of significant figures$1036.48 \text{kg}$.

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 six significant figures-  the five nonzero digits, and zero in middle.

Part (c) step 1: Given Information

We need to find the number of significant figures $4.00 \text{m}$.

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 three significant figures-  the nonzero digits, and the zeroes in the end. 

Part (d) step 1: Given Information

We need to find the number of significant figures ${20.8}^{\circ } \text{C}$.

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 two nonzero digits, and the zeroes in middle. 

Part (e) step 1: Given Information

We need to find the number of significant figures in $60800000 \text{g}$.

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 three significant figures-  the nonzero digits, and one zero  which is in a nonzero digit. The placeholders and, therefore are thus not significant. 

Part (f) step 1: Given Information

We need to find the number of significant figures  $5.0\times {10}^{-3} \text{L.}$

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 two nonzero digits, and the zeroes at the end.