0.1(6) As A Fraction

2 min read Jul 05, 2024

0.1(6) as a Fraction

When we encounter a repeating decimal, such as 0.1(6), it can be confusing to understand how to convert it to a fraction. However, with a few simple steps, we can convert 0.1(6) to a fraction.

What is 0.1(6)?

0.1(6) is a repeating decimal, where the digit 6 repeats indefinitely. This can be written as:

0.166666...

Converting 0.1(6) to a Fraction

To convert 0.1(6) to a fraction, we can use the following steps:

Let x = 0.1(6)

Let's start by letting x equal 0.1(6).

Multiply both sides by 10

Next, multiply both sides of the equation by 10. This gives us:

10x = 1.6(6)

Multiply both sides by 10 again

Now, multiply both sides of the equation by 10 again. This gives us:

100x = 16.6(6)

Subtract the first equation from the second equation

Subtract the first equation from the second equation:

100x - 10x = 16.6(6) - 1.6(6)

This simplifies to:

90x = 15

Divide both sides by 90

Finally, divide both sides of the equation by 90:

x = 15/90

Simplifying the Fraction

We can simplify the fraction 15/90 by dividing both the numerator and the denominator by their greatest common divisor, which is 15. This gives us:

x = 1/6

Conclusion

Therefore, 0.1(6) as a fraction is equal to 1/6.

I hope this helps!