Chapter 1, Problem 1.1CYU

Check Your Understanding Restate $4.79\times {10}^{-\text{5}}\text{ kg}$ using a metric prefix such that the resulting number is bigger than one but less than 1000.

To determine

Restate the number $4.79\times {10}^5\text{kg}$ using metric prefix so that the resulting number should be greater than 1 and smaller than 1000.

Answer to Problem 1.1CYU

The restate number is $479\text{Mg}$.

Explanation of Solution

Given:

Mass, $m=4.79\times {10}^5\text{kg}$

Calculation:

The given mass is $m=4.79\times {10}^5\text{kg}$

First, we need to remove the “kilo” from the given mass

$\begin{array}{c}m=4.79\times {10}^5\times {10}^3\text{g}\\ =\text{4}\text{.79}\times {\text{10}}^8\text{g}\end{array}$

We know that the ${10}^8$ lies between “Mega” and “Giga”, therefore we can use these prefix, however our question demands for a value which is greater than 1 and lesser than 1000, if we use “Giga” prefix the value will come as

$\begin{array}{c}m=\frac{4.79\times {10}^8}{{10}^9}\text{Gg}\\ =\text{0}\text{.479}\text{Gg}<\text{1}\end{array}$

Therefore we have to use “Mega” prefix so that value will between 1 and 1000, the restate value is

$\begin{array}{c}m=\frac{4.79\times {10}^8}{{10}^6}\text{Mg}\\ =\text{479}\text{Mg}\end{array}$

Thus, the restate value of the number is $479\text{Mg}$.

Conclusion:

Restating a number using metric prefix, can convert any value to be fit between 1 and 1000 which is convenient for scientific and engineering calculation.