0.4444 Repeating As A Fraction

Download Article

A repeating decimal, too known as a recurring decimal, is a decimal number that has a digit or digits that infinitely repeat at regular intervals.^[1] Repeating decimals can be tricky to work with, merely they tin too exist converted into a fraction. Sometimes, repeating decimals are indicated by a line over the digits that echo. The number 3.7777 with 7 repeating, for instance, can too be written as 3.7. To convert a number like this to a fraction y'all write it as an equation, multiply, decrease to remove the repeating decimal, and solve the equation.

1
Locate the repeating decimal. For instance, the number 0.4444 has a repeating decimal of 4. It is a basic repeating decimal in the sense that there's no non-repeating portion to the decimal number. Count how many repeating digits there are in the pattern.
- One time your equation is written, you will multiply information technology by x^y, where y equals the number of repeating digits in the design.^[2]
- In the case of 0.4444, there is one digit that repeats, so you lot will multiply the equation by ten^1.
- For a repeating decimal of 0.4545, there are ii digits that repeat, and you would, therefore, multiply your equation by 10^ii.
- For three repeating digits, multiply by ten^three, etc.
ii
Rewrite the decimal equally an equation. Write it out then that x equals the original number. ^[iii] In this instance, the equation is x = 0.4444. Since there's only one digit in the repeating decimal, multiply the equation by 10^i (which equals ten).^[4]
- In the case where x = 0.4444, then 10x = 4.4444.
- With the example 10 = 0.4545, in that location are two repeating digits, and so you multiply both sides of the equation past 10^ii (which equals 100), giving you 100x = 45.4545.
Advertizement
3
Remove the repeating decimal. You lot achieve this by subtracting 10 from 10x. Remember that whatever you exercise to one side of the equation must exist washed to the other, so:^[5]
- 10x – 1x = 4.4444 – 0.4444
- On the left side, you have10x - 1x = 9x. On the right side, you take 4.4444 – 0.4444 = 4
- Therefore, 9x = 4
4
Solve for x. Once you know what 9x equals, you lot can decide what ten equals past dividing both sides of the equation past 9:
- On the left side of the equation you have 9x ÷ 9 = x. On the right side of the equation y'all have 4/9
- Therefore, ten = 4/9, and the repeating decimal 0.4444 can be written every bit the fraction four/nine.
5
Reduce the fraction. Put the fraction in its simplest class (if applicative) by dividing both the numerator and denominator by the greatest common gene.^[six]
- In the case of 4/9, that is the simplest form.

1
Determine the repeating digits. Information technology's not uncommon for a number to have not-repeating digits earlier the repeating decimal, but these can withal exist converted into fractions.^[seven]
- For example, accept the number 6.215151. Here, 6.2 is non-repeating, and the repeating digits are fifteen.
- Once more take note of how many repeating digits there are in the pattern, because you will multiply by x^y based on that number.
- In this example, there are 2 repeating digits, so you lot will multiply your equation past ten^2.
2
Write the problem as an equation and subtract the repeating decimals. Once more, if x = 6.215151, and then 100x = 621.5151. To remove the repeating decimals, subtract from both sides of the equation:^[8]
- 100x – x (= 99x) = 621.5151 - 6.215151 (= 615.3)
- Therefore, 99x = 615.iii
iii

Solve for ten. Since 99x = 615.3, separate both sides of the equation by 99. This gives you x = 615.3/99.
4
Remove the decimal in the numerator. Practise this past multiplying the numerator and denominator by 10^z, where z equals the number of decimal places you lot must motion to eliminate the decimal.^[9] In 615.three, yous have to move the decimal by ane place, meaning you multiply the numerator and denominator by ten^ane:
- 615.iii ten x / 99 x ten = 6153/990
- Reduce the fraction by dividing the numerator and denominator by the highest common cistron, which in this case is 3, giving you ten = two,051/ 330 ^[10]

Add New Question

Question

How exercise I make an improper fraction into a mixed number?

To convert an improper fraction to a mixed number, carve up the denominator into the numerator. The whole number of the quotient is the whole number of the mixed number. If the quotient also has a remainder, the residue is the numerator of the fraction in the mixed number. The denominator of the fraction is the same equally the denominator of the improper fraction. For instance, to catechumen xiii/5 to a mixed number, dissever five into 13. The quotient is 2-three/v. ii is the whole number of the mixed number. three is the numerator of the fraction of the mixed number. 5 is the denominator of the fraction of the mixed number. Thus, the mixed number is two-iii/5 (2 and 3-fifths).
Question

How do I solve a cubic equation?
Question

How practise I prove that the reciprocal of 0.131313 is 7.5?

Actually it'southward not. Use a calculator to divide 1 past 0.131313. Y'all'll get 7.615.

See more than answers

Ask a Question

200 characters left

Include your email address to get a bulletin when this question is answered.

Submit

Advertizing

Video

Thanks for submitting a tip for review!

Near This Article

Article Summary X

To convert repeating decimals to fractions, get-go by writing an equation where x equals your original number. For instance, x = 0.4444. And then, multiply both sides of the equation by 10^1, since there'southward just i repeating digit in your original number, to get 10x = 4.4444. Adjacent, remove the repeating decimal by subtracting ten from 10x on both sides to get 9x = four. Finally, solve for ten to get 4/9. To larn how to convert numbers with repeating and non-repeating decimals, ringlet down!

Did this summary help you?

Cheers to all authors for creating a page that has been read 118,564 times.

Did this article help you?