Question

How do you convert ${\displaystyle \frac{4}{6}}$ into decimals?

Answer 1

Hint: In this problem we have converted ${\displaystyle \frac{4}{6}}$ into decimals. In converting fractions to decimals, we know that decimals are fractions with denominators $10,100,1000$, etc. in order to convert other fractions into decimals, convert the fraction into an equivalent fraction with denominator $10$,$100$ or $1000$ if it is not so. Take the given fraction’s numerator. then mark the decimal point after one place or two-place or three places from right towards left if the given fraction’s denominator is $10$,$100$ or $1000$respectively. But given an expression not like above there given denominator, so we can calculate the given with tables. Then we will cancel the given expression with $2$. Then we will divide that expression.

Complete step by step solution:
Given that, to convert ${\displaystyle \frac{4}{6}}$ into decimals.
Consider the numerator and denominator separately. We have $4$ as a numerator and $6$ as a denominator. We can write $4$ as $2\times 2$ and $6$ as $2\times 3$. Substituting these values in the given fraction, then we will get
${\displaystyle \frac{4}{6}}={\displaystyle \frac{2\times 2}{2\times 3}}$
Canceling the common term in both numerator and denominator which is $2$, then we will get
${\displaystyle \frac{4}{6}}={\displaystyle \frac{2}{3}}$
In the above-simplified fraction, we have a denominator as $3$. We can’t convert the denominator into multiplies of $10$ by multiplying with an appropriate constant. So, it is not possible to get the decimal value in this method. So, we will divide the numerator $2$ with the denominator $3$, then we will get
${\displaystyle \frac{2}{3}}=0.\overline{66}$
The bar above the digits after the decimal point shows that the digits are repeated.

Note: For the given fraction we are unable to convert the denominator into multiples of $10$. So, we have divided the numerator with the denominator. If we are able to convert the denominator in the given fraction into multiples of $10$. Then we need to follow the below examples to write the decimal value.
Example: ${\displaystyle \frac{6}{100}}=0.6$
Similarly, to convert a fraction having $100$ in the denominator, we put the decimals points two places left of the first digit in the numerator.
Example: ${\displaystyle \frac{7}{100}}=0.07$.