Question

How do you convert $0.86$ into a fraction?

Answer 1

Hint: To convert the decimal into fraction, we need to replace the decimal point by ${\displaystyle \frac{1}{100}}$ . The number then becomes ${\displaystyle \frac{86}{100}}$ which can then be further simplified to ${\displaystyle \frac{43}{50}}$ .

Complete step by step solution:
The given that we have at our disposal is,
$0.86$
Decimals are just another way to represent fractions. Instead of writing two numbers above and below a bar, we sometimes prefer to write them as a single number with a decimal point somewhere in between the digits. Decimals are defined by division by $10$ and its multiples. So, $0.1$ means ${\displaystyle \frac{1}{10}}$ , $0.01$ means ${\displaystyle \frac{1}{100}}$ , $0.001$ means ${\displaystyle \frac{1}{1000}}$ and so on.
Decimal to fraction and fraction to decimals conversions are pretty easy. For fractions, if there is $10$ or any of its multiples in the denominator, then conversion to decimal can be done very easily. Also, if we are given a decimal, we first want to remove the decimal point from the number. But the decimal point cannot be removed as per our wish. We have to do something so that even upon removal of the decimal point, the number remains the same. For this, at first, we will count the number of decimal places or the number of digits after the decimal point. We then multiply the number by ${\displaystyle \frac{1}{{10}^n}}$ where n is the number of decimal places and remove the decimal point.
In our case, $n=2$ . So, the decimal becomes,
$0.86=86\times {\displaystyle \frac{1}{{10}^2}}=86\times {\displaystyle \frac{1}{100}}={\displaystyle \frac{86}{100}}$
${\displaystyle \frac{86}{100}}$ can be simplified to ${\displaystyle \frac{43}{50}}$ .
Therefore, we can conclude that the decimal $0.86$ can be converted to ${\displaystyle \frac{43}{50}}$ as a fraction.

Note: Decimal to fraction conversions is very easy but at the same time too prone to silly mistakes. We should be careful to count the number of decimal places in the number as doing it wrong will result in wrong answers. At last, we should also remember to simplify the fraction to the simplest form possible.