Q. 1.27 - An Introduction to General, Organic, and Biological Chemistry

Question

Which number in each of the following pairs is larger? 

a. $7.2 \times {10}^3 or 8.2\times {10}^2$

b.  $4.5 \times {10 }^{-4} or 3.2 \times {10}^{-2}$

c.  $1 \times {10}^4 or 1 \times {10}^{-4}$

d. $0.000 52 or 6.8 \times {10}^{-2}$

Step-by-Step Solution

Answer

a. In this pair $\left(7.2 \times {10}^3 and 8.2 \times {10}^2\right)$ larger number is $7.2 \times {10}^3.$

b. In this pair $\left(4.5 \times {10 }^{-4} and 3.2 \times {10}^{-2}\right)$ larger number is $3.2\times {10}^{-2}$.

c. In this pair  $\left(1 \times {10}^4 and 1 \times {10}^{-4}\right)$ larger number is  $1\times {10}^4$.

d. In this pair  $\left( 0.000 52 and 6.8 \times {10}^{-2}\right)$ larger number is  $6.8\times {10}^{-2}$.

Part (a) step 1: Given Information

We need to find which number $7.2 \times {10}^3 and 8.2 \times {10}^2$ is larger.

Part (a) step 2: Calculation

Convert $7.2\times {10}^3$ to normal notation

$=7200$

Convert $8.2\times {10}^2$ to  normal notation

$=820$

Now,

$7200>820$

So, the larger  is $7.2\times {10}^3$.

Part (b) step 1: Given Information

We need to find which number  $4.5 \times {10 }^{-4} and 3.2\times {10}^{-2}$ is larger.

Part (b) step 2: Calculation

Convert $4.5\times {10}^{-4}$ to normal notation

$=0.00045$

Convert $3.2\times {10}^{-2}$ to normal notation

$=0.032$

Now,

$0.032>0.00045$

So, the larger is $3.2\times {10}^{-2}$.

Part (c) step 1: Given Information

We need to find which number $1 \times {10}^4 and 1 \times {10}^{-4}$ is larger. 

Part (c) step 2: Calculation

Convert $1\times {10}^4$ to normal notation

$=1000$

Convert $1\times {10}^{-4}$  to normal notation

$=0.0001$ 

Now,

$10000>0.0001$

So, the larger is $1\times {10}^4$.

Part (d) step 1: Given Information

We need to find which number $0.000 52 and 6.8 \times {10}^{-2}$is larger.

Part (d) step 2: Calculation

 $0.00052$ on normal notation

$=0.00052$

Convert $6.8\times {10}^{-2}$ to normal notation

$=0.068$

Now,

$0.068>0.00052$

So, the larger is $6.8\times {10}^{-2}$.