How to convert repeating decimals into fractions?

Question

I don't get it!
Why does multiplying n=.72 (repeating 72) by 100 equal 100n=72.72?
If I multiply n=.72 (repeating 72) by 100 I get 100n=72!

And how do you resolve 0.183 (repeating 83) into a fraction?

It's my daughters homework and the examples don't make sense to me. Help!

Answer 1

I am not going into any theories of repeating decimals as the same have already been discussed by the answerers.I would just tell a simple rule to convert the repeating decimal into fraction
I am taking your problem as an example
0.183(83 repeating)
First of all write down the complete no excluding the point as the numerator
Here it is 183() has been ommitted as it has got no value if written at the beginning of the number
Step 2- Subtract from this number (here183),the number which is without recurring .Here 1 is without recurring
so our numerator becomes 183-1=182
Step 3-Now we shall find out the denominator of the fraction.
Count the number of digits with the recurring.Put as many 9s in the denominator.In this case there will be two 9s i.e.99
Step 4.Count the number of digits after the decimal without recurring and put as many zeros after the 9/9s(Remember if there is no digit without recurring after the decimal,no zero is required to be put).In our case,there is only one digit after the decimal,without recurring and so we put only one zero after 99.So our denominator becomes 990
So the fraction formis 182 upon 990 or 182/990(you may reduce it if you like)
some quick practice problem
0.0134 (recurring on 4)
=(134-13)/9000
1.75 (recurring upon 75)
=(175-1)/99
In case of any difficulty you may contact me by a mail through Yahoo Answers

Answer 2

Unless your daughter is in college, you should try just rounding off the value to the nearest hundreths to make the fraction.. There really isnt an easy or shortcut way of doing it coz there really is only one way so ill just explain how it works. for example.. to convert 5 into a fraction, you put /1 beneath to make 5/1 coz u have no decimals.. for 5.25 given two units of decimals that's 5 25/100 or 5 1/4. Following that, the rule is simple. For every movement you make with the decimal, you add a 0 beside the /1 for .25 you move 2 units right and you place 100 beneath.. for .245 you move 3 units to make 245 and you put 1000 below making 245/1000 and you just simplify. For repeating decimals the logic works the same.. that's why you have to just round off or you really wont get an answer.. btw, 100n is not equal to 72! coz 72! is a VERY BIG number... with regards to multiplying, the answer will always repeat.. it's really like that.. you cant change that so i suggest you round off again.. ^_^

Answer 3

In first case when we multiply 0.7272727272..... by 100 ( here note that we are multiplying by 100 because 2 - digits are being repeated and if three digits are reapeated then we should multiply be 1000) , the decimal will be shifted to 2 place right ,Therefore tne 100n = 72.727272....

Q 2) Say n = 0.1838383....... Now multiply the no. by 10 first ,We get
10n = 1.838383........(1) Now again multiply 10n by 100 ( because of the same reason explained earlier)We will get
1000n = 183.838383.........(2)

Now substract (1) from (2) .We get

1000n - 10n = 183.8383....... - 1.838383......
or 990n = 182
or n = 182/990
simplify 182 / 990 we can get n = 91 / 495

Answer 4

Repeating decimals are the result of being divided by s string of 9's. If there a 2 digitd repeting the divisor is 99 if there are three the the divisor is 999 and so on.

.72727272... X 100 = 72.727272...

.183838383... = 1.83838383... / 10 = (1 83/99) / 10 =182/990 = 91 / 495

Answer 5

x=.18383838383...
10x=1.8383838383...
1000x=183.83838383...

subtract:

1000x-10x=183.838383... - 1.838383... = 182

990x=182

x = 91/495