0.8 Repeating As A Fraction

What is 0.8 every bit a fraction? How to convert 0.eight into a fraction? Through the decimal to fraction estimator, we can get the answer of 0.viii to a fraction is 8 9 . Here are two ways to change 0.8 into a fraction.

Eg, convert 0.5xiii to fraction. The trailing decimal place to repeat is 13 and its length is two. So, enter 0.513 into the commencement input box and enter 2 into the 2d input box.

Through the decimal to fraction reckoner folio, we know that there are four steps to convert decimals into fractions:

So, following these 4 steps, nosotros will complete it step by step.

Step 1. Catechumen the decimal to an integer equation.

0.8 contains i trailing decimal place to exist repeated. Permit x is equal to 0.viii, then 10x = viii.8.

10x – x = 8.8 – 0.8
9x = 8

Step 2. Catechumen integer equations into a fraction.

The equation got from Footstep 1, divide both sides by 9 at the same time to get the initial fraction course.

10 = 8 9
0.8 = viii nine

Step iii. Discover the greatest common divisor.

Next, we take to detect the greatest common divisor of 8 and 9.

The factors of viii are ane, 2, 4, eight.

The factors of ix are one, iii, 9.

And then, the greatest common divisor of 8 and 9 is one.

GCD(eight, nine) = ane

Step iv. Simplify the fraction

Now, we accept found that the greatest common divisor of 8 and 9 is 1. So, the initial fraction is the most simplified fraction.

0.eight = 8 9

So, the reply of 0.8 every bit a fraction is 8 nine .

This is the routine conversion procedure from decimal to fraction. Is there a simpler 1? Let's accept a look at the following method.

Infinite Recurring Decimals to Fractions Formula 1
Obviously, 0.8 is an infinite recurring decimal, and the decimal point is immediately followed by the trailing decimal places to be repeated. The length of trailing decimal places to be repeated is 1. Through the infinite recurring decimal to fraction formula, nosotros can get that the initial denominator of the fraction is 9 and the initial numerator is 8 – 0 = viii. So the initial class of the fraction is 8 9 .

The side by side steps are the same as Method 1. Notice the greatest mutual divisor of eight and 9 is 1, then simplify the initial fraction. The terminal answer is also 8 ix .

Comparing these two methods, both methods tin can calculate the fraction of 0.8, but the second formula method is relatively elementary and tin can get the initial form of the fraction in one step.

Finally, tell you a piffling trick which tin can salve all the calculation steps. This is directly using the online complimentary decimal to fraction estimator we provide. Both finite and infinite decimals can exist easily converted to fractions. Of course, the concluding fraction is simplified. It tin can exist an improper fraction or a mixed fraction. Everyone is welcome to utilise!