Need help converting decimals to fractions and vice versa

sheana11
sheana11 used Ask the Experts™
on
I came across the following:


"If the distance estimated at 150 feet is really 140 ft, the percent of error in this estimate is 7 1/7%."

Can you tell me how this answer was expressed as a fraction? I get 7.1428%. How is the .1428 converted to 1/7?

Please demonstrate how you computed it. Thanks.
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Keep the 7. Then divide 1/.1428  It's close to 7. An approximation for the denominator.

Similarly, to get the decimal, just divide 1 by 7.
You are off by 10. Your percent off is 10/140 or 1/14. so divide (long division)
!@#!! You cannot show it easily here.

                  7
         _____________
14    |   100
               98
             _____
                 2


and stop here so that the remainder is 2/14   which = 1/7
I think it is off less than that. You starting point is 150 feet not 140 feet.
If the estimate was 150 and it came in at 140 that's 10 feet less.

10/150 = 6.6666667%

10/150 = 1/15

1/15 x 100% = yes, you guessed it, 6.6666667%)
So the reverse math works.

Any % you have regardless of the number is x divided by 100.
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Commented:
well the formula is  100*|measured - actual|/actual  (the 100 is to turn it into a percent)

so we have


100*|measured - actual|/actual =   100*|150-140|/140 = 100*10/140 = 100/ 14  = (14*7+2)/14     =   14*7/14  + 2/14   = 7 + 2/14 = 7 + 1/7 = 7 and 1/7 as they have.

So why did I replace   100 by   14*7 + 2 in the second line?

well the denominator (14) can be at most multiplied 7 times without being bigger than the numerator (100). 2 is the remainder.

Also .1428 cannot be converted to 1/7.


1/7 is the correct result.  Though you can approximate 1/7 by .1428.
Although 1/7 is a rational number,  decimals are always sums of numbers being divided by powers of 10 (hence the word decimal). Here however we're dividing by 7, and when we use fractions with something other than a power of 10 in the denominator then often all we can do is use a decimal approximation for the fraction.




Does this help?
sheana11
I came across the following:
"If the distance estimated at 150 feet is really 140 ft, the percent of error in this estimate is 7 1/7%."

sheana11 are you wanting to know the amount of distance that was lost or gained.

The estimated distance was 150 feet. Right?
Actual feet came in at 140.

The actual is 150 - 140 = 10 / 150 = 6.666667%.
The actual length came in that % below the estimate.

It depends on what you wish know. If you wish to know how much shorter was the actual length as compared to the estimate of 150 feet, then that is the 6.666667% or .06666667.

The actual measurement was 140 feet. Your estimate was 150 feet and "that is" 7.1284% higher than the actual.
And the actual was 6.666667% lower than the estimate.
awking00Information Technology Specialist

Commented:
1/7 = .142857
1/.1428 = 7.002801

Commented:
Do you agree that saying 7 1/7 is equivalent to saying 7 + 1/7  

1 divided by 7, using long division, you come up with 1428. In other words, 1/7 equals .1428.

So, that is the same as saying 7+.1428%, or simply 7.1428%...

All you are doing is changing 1/7 to a decimal by using division to express the exact same thing in decimal, rather than fraction.

7 1/7% = 7.1428%

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