17 Repeating As A Fraction

What is 0.1vii every bit a fraction? How to convert 0.17 into a fraction? Through the decimal to fraction calculator, we tin can get the reply of 0.17 to a fraction is eight 45 . Hither are ii means to change 0.1vii into a fraction.

Eg, convert 0.5thirteen to fraction. The trailing decimal identify to echo is xiii and its length is two. So, enter 0.513 into the get-go input box and enter 2 into the second input box.

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

So, following these four steps, we volition complete it pace past stride.

Stride 1. Convert the decimal to an integer equation.

0.17, the decimal bespeak is followed past an non-recurring decimal place of i, and so followed past a repeating trailing decimal identify of 7. Let ten = 0.17, then 10x = ane.7, 100x = 17.vii.

100x – 10x = 17.7 – 1.7
90x = 16

Step two. Catechumen integer equations into a fraction.

The equation got from Step one, split both sides by 90 at the aforementioned fourth dimension to become the initial fraction grade.

x = 16 ninety
0.iseven = xvi 90

Step 3. Detect the greatest common divisor.

Adjacent, nosotros have to notice the greatest common divisor of 16 and xc.

The factors of 16 are 1, 2, 4, viii, sixteen.

The factors of xc are 1, 2, 3, five, 6, nine, 10, 15, xviii, xxx, 45, 90.

Then, the greatest common divisor of sixteen and xc is 2.

GCD(16, ninety) = ii

Step four. Simplify the fraction

Now, we accept establish that the greatest common divisor of xvi and xc is 2. Therefore, the numerator and denominator of the initial fraction are divided past ii to get the final simplified fraction.

0.i7 = 16 90
= 16 ÷ ii ninety ÷ two
= 8 45

Then, the answer of 0.17 as a fraction is viii 45 .

This is the routine conversion process from decimal to fraction. Is there a simpler one? Permit's take a look at the following method.

Infinite Recurring Decimals to Fractions Formula 2
Obviously, 0.17 is an space recurring decimal, there are non-recurring decimals and recurring decimals subsequently the decimal point. The length of the not-recurring decimal places is 1, and the length of the trailing decimal places to be repeated is 1. Through the infinite recurring decimal to fraction formula, we can become that the initial denominator of the fraction is 90 and the initial numerator is 17 – 1 = 16. So the initial form of the fraction is 16 90 .

The next steps are the same every bit Method i. Discover the greatest mutual divisor of xvi and 90 is ii, then simplify the initial fraction. The final answer is also 8 45 .

Comparing these 2 methods, both methods can calculate the fraction of 0.1vii, but the second formula method is relatively simple and tin get the initial form of the fraction in one step.

Finally, tell y'all a petty trick which can save all the calculation steps. This is directly using the online free decimal to fraction figurer we provide. Both finite and infinite decimals tin can be easily converted to fractions. Of course, the final fraction is simplified. It tin can be an improper fraction or a mixed fraction. Everyone is welcome to apply!