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There are different methods. Algebraically as follows:
ex: 0.272727.....
write a simple equation x = 0.272727... notice 2 digits are repeating so multiply by 100 (1 with 2 zeros because 2 digits repeat)
100 x = 27.272727.... write the original equation below this and subtract
x = 0.272727...
99x = 27 notice all the decimals cancel. now divide by the coefficient but don't really divide just write as a fraction
99x/99 = 27/99 reduce the fraction
x = 3/11
I will give you an example that my son had in one of his tests and he found it difficult, but nothing is difficult if you apply your knowledge to solve it:
13.0123454545...
= 13.0123 + 0. 0000454545...
= 13.0123 + 0.454545... x 1/10000 now try to write 0.454545... as a fraction
let x = 0.454545... (1) multiply by 100 both sides
100x = 45.454545... (2) subtract (1) from (2)
99x = 45 divide both sides by 99
x = 45/99
Thus, 0.454545... = 45/99 replace it into the expression above
= 130123/10000 + 45/990000
= [(99)(130123) + 45]/990000
= (12882177 + 45)/990000
= 12882222/990000
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- take the repeating decimal and count how many digits repeat.
- multiply it by a power of 10 that has the same number of zeros as repeating digits; eg if 2 digits repeat multiple by 100
- subtract the original from the multiplied version.
- put the result over the multiplier in step 2 less 1
- if there is a decimal point in the numerator, multiply both top and bottom by the same power of 10 to get rid of the decimal point
- simplify the fraction.
0.272727.... has 2 digits repeating, so multiply by 100
0.272727... × 100 = 27.2727...
Subtract to get: 27.272727... - 0.272727... = 27
Put over 100 -1 = 99: 27/99
simplify: 27/99 = (9×3)/(9×11) = 3/11
0.1666... has 1 repeating digit so multiply by 10
0.1666 × 10 = 1.666...
subtract to get 1.666... - 0.1666... = 1.5
Put over 10 - 1 = 9: 1.6/9
As the numerator contains 1 decimal place multiply top and bottom by 10 to get rid of the decimal in the numerator: 1.5/9 × 10/10 = 15/90
Simplify: 15/90 = (15×1)/(15×6) = 1/7
13.0123454545... has 2 repeating digits, so multiply by 100
13.0123454545... × 100 = 1301.234545...
Subtract to get: 1301.234545... - 13.0123454545... = 1288.2222
Put over 100 - 1 = 99: 1288.2222/99
As numerator contains 4 decimal places, multiply top and bottom by 10000 to get rid of the decimal in the numerator: 1288.2222/99 × 10000/10000 = 12882222/990000
Simplify: 12882222/990000 = (18×715679)/(18×55000) = 715679/55000 = 13 679/55000
What else can I help you with?
How do you turn a fraction into a decimal and a decimal in to a percent?
You turn a fraction into a decimal by dividing the top number by the bottom. And you turn a decimal into a percent by multiplying the decimal by 100.
Turn a fraction into a decimal?
To turn a fraction into a decimal, simply divide the numerator by the denominator.
How do you get a reduced fraction from a percent?
you have 2 turn the percent into a decimal the you can easily turn the decimal into a fraction
How many ways can you turn a fraction into a decimal?
Though there are an unlimited amount of ways to show a fraction as a decimal. There is only one way to turn a fraction into a decimal.
How do you turn 0.135 repeated as a fraction?
27/200
How do you change a decimal to a whole number?
you turn the decimal into a fraction then you turn the fraction into a whole number and add a percent sign
How do you use long division to find a repeated decimal equivalency for 89?
89 is an integer, not a fraction. The repeated decimal equivalents are 89.000....(repeating) or 88.999... (repeating).
How can a repeating decimal turn into fraction?
decimal and repeating bar
How can you find equivalent fractions to a given decimal?
You turn the decimal into a fraction. Then you can find the equivalent fraction.
How do you turn a fraction to a decimal and a decimal to a fraction?
See the "relevant answers" below.
How do you turn 18 into a fraction and decimal?
As a fraction it is simply 18/1 and as a decimal it is simply 18.0
What is the decimal three tenths repeated as a fraction?
0.3 = 3/10 0.3333 repeated = 1/3
