Q. 1.28 - An Introduction to General, Organic, and Biological Chemistry

Question

Which number in each of the following pairs is smaller? 

a.  $4.9\times {10}^{-3} or 5.5\times {10}^{-9}$

b. $1250 or 3.4 \times {10}^2$

c.  $0.000 000 4 or 5.0\times {10}^2$

d.  $2.50 \times {10}^2 or 4 \times {10}^5$

Step-by-Step Solution

Answer

a. In this pair $\left(4.9 X {10}^{-3} and 5.5 X {10}^{-9}\right)$ smaller number is $5.5 \times {10}^{-9}$.

b. In this pair $\left(1250 and 3.4 \times {10}^2\right)$ smaller number is $340$.

c. In this pair $\left(0.000 000 4 and 5.0\times {10}^2\right)$ smaller number is  $0.000 000 4$.

d. In this pair $\left(2.50 \times {10}^2 and 4\times {10}^5\right)$ smaller number is  $2.50 \times {10}^2$.

Part (a) step 1: Given Information

We need to find which number $4.9 \times {10}^{-3} and 5.5 \times {10}^{-9}$ is smaller.

Part (a) step 2: Calculation

Convert $4.9\times {10}^{-3}$ to normal notation

$=0.0049$

Convert $5.5\times {10}^{-9}$ to normal notation

$=0.0000000055$

Now,

$0.0049>0.0000000055$

So, the smaller is $5.5\times {10}^{-9}$.

Part (b) step 1: Given Information

We need to find which number $1250 and 3.4\times {10}^2$ is smaller. 

Part (b) step 2: Calculation

$1250$ is already in normal notation

Convert $3.4\times {10}^2$ to normal notation

$=340$

Now,

$1250>340$

So, the smaller is $3.4\times {10}^2$.

Part (c) step 1: Given Information

We need to find which number  $0.000 000 4 and 5.0 \times {10}^2$is smaller. 

Part (c) step 2: Calculation

$0.0000004$ is already in normal notation

=$0.0000004$

Convert $5.0\times {10}^2$ to normal notation

=$500$

Now,

$500>0.0000004$

So, the smaller is $0.0000004$.

Part (d) step 1: Given Information

We need to find which number $2.50 \times {10}^2 and 4 \times {10}^5$is smaller.

Part (d) step 2: Calculation

Convert $2.5\times {10}^2$ to normal notation

$=250$

Convert $4\times {10}^5$ to normal notation

$=400000$

Now,

$40000>250$

So, the smaller is $2.5\times {10}^2$.