Chapter 5.3, Problem 12OE

To determine

To Find: Blank space to make a statement true.

Answer to Problem 12OE

  $2.78\times {10}^{-4}$ $>$ $2.78\times {10}^{-6}$

Explanation of Solution

Given information:

  $2.78\times {10}^{-4}$ $\underset{\_}{?}$ $2.78\times {10}^{-6}$

  $2.78\times {10}^{-4}$ $\underset{\_}{?}$

  $2.78\times {10}^{-6}$ $2.78\times {10}^{-6}$ can be written as

  $\begin{array}{l}2.78\times {10}^{-6}=2.78\times {10}^{-2}\times {10}^{-4}\\ \Rightarrow 2.78\times {10}^{-6}=2.78\times \frac{1}{{10}^2}\times {10}^{-4}\\ \Rightarrow 2.78\times {10}^{-6}=2.78\times \frac{1}{100}\times {10}^{-4}\\ \Rightarrow 2.78\times {10}^{-6}=0.0278\times {10}^{-4}\end{array}$

As both numbers have ${10}^{-4}$ common we only need to compare remaining part of the numbers.

On comparing $2.78$ and $0.0278$ we can say that

  $2.78$ is greater than $0.0278$ .

Therefore,

  $2.78\times {10}^{-4}$ $>$ $2.78\times {10}^{-6}$