Chapter 2.2, Problem 28SSC

Interpretation Introduction

Interpretation: The given value in kilometers needs to be converted into millimeters.

Concept introduction: The action of measuring the size or quantity of anything is defined as a measurement. Dimensional analysis is utilized to convert a set of units into another set of units.

Answer to Problem 28SSC

$\text{2}{\text{.5 ×10}}^{\text{2}}\text{km}=\text{2}{\text{.5 ×10}}^{\text{8}}\text{mm}$

Explanation of Solution

Dimensional analysis is a problem-solving method. With the help of this, a scientist converts the unit of measurement that is taken by him/her.

The formula to convert kilometers to millimeters is given below:

$1mm={10}^{-6}km$

The given value is:

$\text{2}{\text{.5 ×10}}^{\text{2}}\text{ km}$

Thus,

$\frac{\text{2}{\text{.5 ×10}}^{\text{2}}\text{ km}\left(1\text{ mm}\right)}{{10}^{-6}\text{ km}}=2.5\times {10}^8\text{ mm}$

So, $\text{2}{\text{.5 ×10}}^{\text{2}}\text{km=2}{\text{.5 ×10}}^{\text{8}}\text{mm}$

Conclusion

Thus,

$\text{2}{\text{.5 ×10}}^{\text{2}}\text{km=2}{\text{.5 ×10}}^{\text{8}}\text{mm}$