Question

What is 16.2 divided by 0.002?

Answer 1

Hint: Here is the division by decimal point number. But easily we can do this. Easily we can multiply decimals by power of$10$. Count the decimal points at numerator and denominator. Find which one’s decimal is biggest. And then multiply the tenth power of the biggest decimal point at both numerator and denominator.

Complete step-by-step solution:
The given problem is ,
 $16.2 \div 0.002$.
First we find the value of $0.002$
There are three digits after the decimal point. When we remove the decimal point that point comes as a denominator of power of ten. The next step is removing the one point it comes in the denominator as ${10^1}$.
$0.002 = 0.02 \times \dfrac{1}{{10}}$
In this step we remove the two points. In the denominator we have${10^2}$.
$0.002 = 0.2 \times \dfrac{1}{{10}} \times \dfrac{1}{{10}}$
We remove all of the three decimal points and we get the denominator as${10^3}$.
$0.002 = 2 \times \dfrac{1}{{10}} \times \dfrac{1}{{10}} \times \dfrac{1}{{10}}$
Here the value of $0.002$is,
$0.002 = 2 \times \dfrac{1}{{1000}}$
Here we found the value of $0.002$and now we substitute the value in the given problem .we get
$16.2 \div 0.002 = 16.2 \div \left( {2 \times \dfrac{1}{{1000}}} \right)$
Here $16.2$ is divided by $2$. And we get the value $8.1$
And the value is again divided by 1000
$16.2 \div 0.002 = 8.1 \div \left( {\dfrac{1}{{1000}}} \right)$
$16.2 \div 0.002 = 8.1 \times 1000$
Hence the answer for the problem is,
$16.2 \div 0.002 = 8100$.

Note: By using the hint we have to solve the problem in an easy way. The division of multiple is the biggest problem. But easily we need to multiply the numerator and denominator as the same number of tenth powers. Compare the decimal points of numerator and denominator. And find which one is the bigger. Take that value as power of 10.from the given problem,
At the numerator we have one valve after the decimal point.
At the denominator we have three values after the decimal point. Therefore the denominator has the biggest value. So multiply the numerator and denominator by ${10^3}$.we have,
$ = \dfrac{{16.2 \times {{10}^3}}}{{0.002 \times {{10}^3}}}$
Expand the power of ten, we get,
$ = \dfrac{{16.2 \times 10 \times 10 \times 10}}{{0.002 \times 10 \times 10 \times 10}}$
Here ten power cubes is equal to thousand,
$ = \dfrac{{16.2 \times 1000}}{{0.002 \times 1000}}$
$ = \dfrac{{16200}}{2}$
Divide the value we get the answer.
$ = 8100$