Question

What is 0.46 repeating as a fraction?

Answer 1

Hint: As we know that fraction is in the form of a numerator and denominator. Here we will first multiply the number above by 100. Then we will subtract the results so found. And then we can express it in fraction form.

Complete step by step answer:
Given that, 0.46 is a repeating fraction.
\[x = 0.\bar 4\bar 6\]
Now we will multiply both sides by 100,
\[100x = 46.\bar 4\bar 6\]
Now we will subtract the above two expressions,
\[100x - x = 46.\bar 4\bar 6 - 0.\bar 4\bar 6\]
On subtracting we get,
\[99x = 46\]
On transposing the numbers only we get,
\[x = \dfrac{{46}}{{99}}\]
Thus this is the repeating number that is expressed as fraction.

Note:
Here note that if the given number is a repeating number and only one term is repeating after decimal then we only need to multiply it by 10 to express it in fraction form. Also note that if the fraction is not in simplified form then we have to simplify it.