what is 4.16 repeating as a fraction
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
\(4\frac{1}{6} = \frac{25}{6}\)