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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.
How can a repeating decimal turn into fraction?
decimal and repeating bar
What is the fraction of the repeating decimal 0.7...?
The fraction of the repeating decimal 0.7... is 7/9
Is the fraction 13 a terminating or repeating decimal?
It is a repeating decimal.
How do you convert 0.2 a repeating decimal into a fraction?
0.2 a repeating decimal into a fraction = 2/9
How do you write the repeating decimal 1.1 as a fraction?
repeating decimal 1.1 as a fraction = 10/9
Answer to 2.535353 turn into fraction?
If that is a terminating decimal, it is 2 535353/1000000 (as a mixed number) = 2535353/1000000 (as an improper fraction) If that is a repeating decimal 2.535353... with the 53 repeating, it is 2 53/99 = 251/99
How do you turn 74.6666 into a fraction?
If it's a 6 repeating decimal then it is 224/3 if not then it is 746666/10000
What is 1.142857 repeating as a fraction?
Oh, what a happy little question! When we see a repeating decimal like 1.142857, we can turn it into a fraction by noting that the repeating part is 142857. To convert this to a fraction, we put this repeating part over a series of nines equal to the number of repeating digits, which gives us 142857/999999. And just like that, we've turned our repeating decimal into a lovely fraction.
How do you turn a division into a decimal fraction?
You do a long division, adding decimal digits until you get a remainder of zero (terminating decimal) or a repeating pattern of decimal digits.
Turn 2.3 repeating into a decimal please?
2.3 repeating is already a decimal. It would look like this: 2.33333333333333... If you want a rounded decimal, you can use 2.3. However, 2.3 repeating would be more useful as a fraction for proportions and things. As a fraction, it is 2 1/3 (two and one third).
How do you determine whether you can write a given decimal as a fraction?
If the decimal is terminating or repeating then it can be written as a fraction. Decimal representations which are non-terminating and non-repeating cannot be expressed as a fraction.
How can a decimal greater than 1 be a repeating decimal?
A decimal number is like a mixed fraction: it has an integer part and a fractional part. If the fractional part is a repeating fraction then the whole number is represented by a repeating decimal.
