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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
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A repeating decimal is an irrational number?
Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.
How can you turn 1 over 15 as a decimal?
0.06666 repeating
How do you write 1.571429 as a fraction?
I assume that the decimal part is repeating to infinity. Then 1.571429 written as a fraction is 1 and 4/7.
What is 0.12333 in fraction form?
0.12333 = 12333/100000, unless you want the repeating decimal (33333.....) then the fraction is equivalent to 37/300.
What is 5 repeating into a fraction?
To convert a one digit repeating decimal, make a fraction of that digit over 9, so 55/99 = 5/9 You can convert any repeating digits by putting them over the same number of 9s.
