Question

What is $.67$ as a simplified fraction?

Answer 1

Hint: Here in this question we have been asked to write the given number $.67$ as a simplified fraction. For answering this question we will first write it down the decimal number $.67$ as divided by 1 that is ${\displaystyle \frac{.67}{1}}$ and then as we have 2 digits after the decimal point in the numerator, we need to multiply both numerator and denominator by ${10}^2=100$, so that there will be no decimal point in the numerator.

Complete step-by-step solution:
Now considering from the question we have been asked to write the given number $.67$ as a simplified fraction.
From the basic concepts we know that a fraction is not a whole number but a number between the whole numbers which is a part of a whole and has two parts, a numerator and a denominator.
For answering this question we will first write it down the decimal number $.67$ as divided by 1. We can also write $.67$ as $0.67$. By doing this we will have $\Rightarrow {\displaystyle \frac{0.67}{1}}$
Now as we have 2 digits after the decimal point in the numerator, we need to multiply both numerator and denominator by ${10}^2=100$, so that there will be no decimal point in the numerator. By doing that we will have $\Rightarrow {\displaystyle \frac{0.67\times 100}{1\times 100}}={\displaystyle \frac{67}{100}}$ .
Now we need to write this number ${\displaystyle \frac{67}{100}}$ in the simplest form. As we know that 67 is a prime number that is it is only divisible by 1 and itself. Hence there are no common multiples for numerator and denominator except 1 so this is the simplest form.
Therefore we can conclude that the given number $.67$ can be represented as a simplified fraction as ${\displaystyle \frac{67}{100}}$.

Note: While answering questions of this type we should be sure with the concepts that we are going to apply and the calculations that we are going to perform in between the steps. Fractions and decimals are two different ways of representing numbers they can be converted from one form to the other. A fraction can be converted into a decimal by simply dividing the numerator with the denominator.