how do you change a repeating decimal or any decimal into a fraction???

Question

like for example 0.6 repeating or 0.35 and0.375 0.6

Answer 1

x=0.66666666666.........................................
10x=6.666666666.........................................
subtracting 1 from 2
9x=6
x=6/9=>2/3

2.0.35
=35/100
7/20

3.0.37506
=37506/100000
=18753/50000

Answer 2

Repeating decimal, there's a very nice trick.

For example the repeating decimal is 0.6666. The repeating element here is 6. Then the fraction is 6/9.

Or another example, 0.2323232323... = 23/99. 0.200620062006... = 2006/9999. Check it out.

The rule for this is, the numerator is the repeating element and the denominator is a number that consists of only 9's. The number of 9's equals to the length of the repeating element.

Answer 3

Decimal is a representation of tenths, hundredths, so any decimal begins over some power of 10

e.g. 35/100. You then simplify the fraction to 7/20 (simplified by 5 in this case).

.6 is read as six-tenths, so it starts out as 6/10. Simplified by 2, it becomes 3/5.

.375 starts as 375/1000. I'll let you simplify it.

I can't help with the repeating decimal example.

Answer 4

the decimal is say (0.66666)/(1.0) which basically is a fraction, then you have to multiply the top and bottom of the fraction by integers untill the top is an integer So
(0.6666)/(1.0) * (6.0)/(6.0) = (3.9999)/(6.0) which is approxamatly
4/6 or 2/3 which is the correct answer.

multiplying the top and the bottom by the same number say 6/6 is ok to do and doesn't break any "rules"

Answer 5

single digit repeating .. divide by 9.
ie 0.66666666.... is 6/9 = 2/3
or 0.33333333333333 is 3/9 or 1/3

two digits repeating divide by 99
ie 0.353535.... is 35/99

Answer 6

x = 0.1234567891...
10^9 x = 123456789.1234567891... = 123456789 + x
10^9 x - x = 123456789
(10 ^ 9 -1 ) x = 123456789
x = 123456789 / (10 ^ 9 - 1)

Answer 7

buy a calculator!!