0.4 Repeating As A Fraction

What is 0.vii4 as a fraction? How to convert 0.74 into a fraction? Through the decimal to fraction figurer, we can get the reply of 0.74 to a fraction is 67 xc . Here are two ways to alter 0.74 into a fraction.

Eg, convert 0.v13 to fraction. The trailing decimal place to echo is xiii and its length is 2. Then, enter 0.513 into the beginning input box and enter ii into the second input box.

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

And then, following these 4 steps, we volition complete it step past step.

Step 1. Convert the decimal to an integer equation.

0.7four, the decimal point is followed by an non-recurring decimal place of 7, and then followed by a repeating trailing decimal identify of iv. Let x = 0.74, then 10x = 7.four, 100x = 74.4.

100x – 10x = 74.4 – 7.4
90x = 67

Step two. Convert integer equations into a fraction.

The equation got from Step 1, split both sides by 90 at the same time to get the initial fraction course.

ten = 67 90
0.74 = 67 90

Stride three. Find the greatest common divisor.

Next, we accept to notice the greatest common divisor of 67 and xc.

The factors of 67 are one, 67.

The factors of 90 are 1, 2, 3, v, 6, 9, 10, fifteen, 18, 30, 45, ninety.

So, the greatest common divisor of 67 and xc is 1.

GCD(67, 90) = ane

Step 4. Simplify the fraction

Now, we accept found that the greatest common divisor of 67 and xc is i. So, the initial fraction is the most simplified fraction.

0.vii4 = 67 90

So, the respond of 0.74 as a fraction is 67 90 .

This is the routine conversion process from decimal to fraction. Is at that place a simpler ane? Let'southward have a look at the post-obit method.

Infinite Recurring Decimals to Fractions Formula 2
Obviously, 0.74 is an infinite recurring decimal, there are non-recurring decimals and recurring decimals after the decimal signal. The length of the not-recurring decimal places is one, and the length of the abaft decimal places to exist repeated is i. Through the infinite recurring decimal to fraction formula, we tin become that the initial denominator of the fraction is 90 and the initial numerator is 74 – 7 = 67. So the initial grade of the fraction is 67 90 .

The next steps are the same as Method one. Find the greatest common divisor of 67 and 90 is ane, and so simplify the initial fraction. The final answer is also 67 90 .

Comparison these two methods, both methods tin calculate the fraction of 0.viifour, merely the second formula method is relatively unproblematic and tin can go the initial form of the fraction in one step.

Finally, tell you a lilliputian trick which can salvage all the calculation steps. This is directly using the online gratis decimal to fraction calculator nosotros provide. Both finite and infinite decimals tin be hands converted to fractions. Of course, the final fraction is simplified. It can be an improper fraction or a mixed fraction. Everyone is welcome to employ!