Math Is Fun Forum

Hannibal lecter

Member

Registered: 2016-02-11

Posts: 393

division over 1/7

hi, 1/7 is a ecurring decimal mean it's move forver infinitiy right?
if I want to represt 1.5 as a length  like 1.5 meter or 2 meter or 0.5 meter
it's easy

but how to represent the 1.7 as meter let say there is a stick its length is 1.7 meter! is that possible?

and can I divive the recuring decimal over other numbers? like 1/7 divided by 3

can exmplain more pls about how to treat these ecurring decimal numbers or is there textbooks explain these to me

Last edited by Hannibal lecter (2025-12-07 23:31:21)

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Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 52,664

Re: division over 1/7

Hi,

1/7 is a recurring decimal.

.

See the links.

Converting fractions to decimals.

Recurring Decimals.

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Bob

Administrator

Registered: 2010-06-20

Posts: 10,804

Re: division over 1/7

Every recurring decimal can be represented by a fraction.  I'll show how by doing an example:

Firstly you need to separate any decimal figures that are not part of the recurring part. Those are easily dealt with separately.

Then you can use a 'sum to infinity' trick on the recurring part.

Finally combine the two parts to make the final fraction.

eg.  0.741212121212......

Split into 0.74 and 0.001212121212.....

0.74 is 74/100 so that's easily sorted.

let a/b - 0.00121212121212..........                           (1)

As there are 2 recurring digits multiply this by 100.  (n recurring digits multiply by 10^n)

100a/b = 0.1212121212121212.....                           (2)

Subtract (1) from (2). This removes the recurring bit completely.

99a/b = 0.12      Convert this to an integer only equation.

9900a/b = 12 

This means that a/b =  12/9900

Now recombine the two fractions:

74/100 + 12/9900  = ( 7326 + 12 )/9900 = 7338/9900

Bob

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Phrzby Phil

Member

From: Richmond, VA

Registered: 2022-03-29

Posts: 66

Re: division over 1/7

I never thought about this problem Bob - you learn something every day if you're lucky.

Thanks.

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