Repeated decimals can be converted into fractions by shifting the decimal to the right and subtracting the decimals. To do this, multiply the number by 10 to the second power, then subtract. For example, 0.363636 repeating is 4/11 and 0.7141414 repeating is 707/990.
Answer: 0.33333 as a fraction is 1/3
Now that you know that . 33333 as a fraction is 1/3, lets explore why this math fact is true.
A repeating decimal can always be written as a fraction using algebraic methods that are beyond the scope of this article. However, it is important to recognize that any decimal with one or more digits that repeats forever, for example ...
Answer and Explanation: As a fraction, 5.33333333333 can be expressed either as 5 1 3 o r 16 3 .
So we can see that our original decimal of 0.333333... is equal to the fraction 1/3.
Solution: 0.124 as a fraction is 31/250.
Solution: 7.4 as a fraction is 37/5.
Solution: 1.29 as a fraction is 129/100.
Solution: 25% as a fraction is 1/4.
First, we can recognize that 0.16666666666 is approximately equal to 1/6.
So 0.142857142857… is equal to 142,857/999,999 which, believe it or not, after dividing both the top and bottom by 142,857 is equal to the fraction 1/7!
Solution: 0.66666 as a fraction is 33333/50000.
Solution: 3.6 as a fraction is 18/5.
Solution: 4.8 as a fraction is 24/5.
Answer: 7.5 as a fraction is 15/2.
To convert a decimal number into a fraction, we write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly. Then, this fraction can be simplified.
For example, 0.123123123. . . is a repeating decimal; the “123” will repeat endlessly. Any repeating decimal is equal to a rational number. For example, 0.123123. . . is equal to 123/999, or 41/333.
Solution: 0.347 as a fraction is 347/1000.
Solution: 13.74 as a fraction is 687/50.
The fraction represented by the decimal 0.666666666667 is 2/3.
∴ Fraction form of the decimal 0.037037037.... is 127.
Expressed as a geometric series: 0.11111 ⋯ = 1 / 10 + 1 / 100 + 1 / 1000 + 1 / 10000 + ⋯ = ( 1 / 10 ) ( 1 + 1 / 10 + 1 / 100 + 1 / 1000 + … ) So we found the repeating decimal 0.11111 … equal to one-ninth.