Question

What is 9.0 divided by 0.9?

Answer 1

Hint: We are asked to find the result of 9.0 divided by 0.9. We can perform this by multiplying and dividing 10 to the denominator so that we will be dealing only with integers and the answer can be found easily after this step.

Complete step by step solution:
In the question, we have been asked to find the value of 9.0 divided by 0.9 . Whenever we are dealing with decimals, it is best to convert them in to integers if possible. This way, we can easily compute the required result. We are asked to find the value of ${\displaystyle \frac{9.0}{0.9}}$ .
First, let us convert the denominator, 0.9 into an integer. For that we must multiply and divide by 10. Doing so, we get,
${\displaystyle \frac{9.0\times 10}{0.9\times 10}}={\displaystyle \frac{90}{9}}$
Hence, we can clearly see that we have gotten rid of the decimal point and we are left with only integer division. Now, finally we can find the required result using division.
$\begin{array}{rl}& {\displaystyle \frac{90}{9}}={\displaystyle \frac{9\times 10}{9}}\\ & \Rightarrow {\displaystyle \frac{90}{9}}=10\end{array}$
Therefore, the result of 9.0 divided by 0.9 is found to be 10.

Note: When we multiply and divide 10 to both numerator and denominator, we must first check how many decimal places are present. If there are more than 1, accordingly we should multiply a higher power of 10. For example, if we were given the fraction ${\displaystyle \frac{9}{0.009}}$ , we can clearly see that there are 3 decimal places present in the denominator. Hence we must multiply and divide 10 to the power 3, doing so we get,
$\begin{array}{rl}& {\displaystyle \frac{9\times {10}^3}{0.009\times {10}^3}}={\displaystyle \frac{9000}{9}}\\ & {\displaystyle \frac{9000}{9}}=1000\end{array}$
Hence, one must decide what to multiply and divide by checking the decimal places properly.