Question

What is 4.16 repeating as a fraction

Answer 1

4.16=416/100
416/100=4•104/4•25
=104/25
4.16=104/25

Answer 2

Answer:

4.16 = $4\frac{1}{6} = \frac{25}{6}$

Step-by-step explanation:

The given number is 4.16 repeating.

Here the whole number part is 4

4.16 repeating = 4 + 0.166...

Let's take the decimal part 0.166...

Let's assume x = 0.166...

Multiply by 10, we get

10x = 1.66...

Multiply by 100, we get

100x = 16.66...

Now let's subtract

100x - 10x = 16.66... - 1.66...

90x = 15

Divide both sides by 90, we get

x = $\frac{15}{90}$

Now let's reduce the fraction by dividing both the numerator and the denominator by 15, we get

x =$\frac{1}{6}$

Now let's add the whole number part 4 and the fraction $\frac{1}{6}$

$4 + \frac{1}{6} = 4\frac{1}{6}$

We can convert this mixed number to improper fraction

$4\frac{1}{6} = \frac{25}{6}$