Converting decimals to fractions

  • Thread starter Cliff Hanley
  • Start date
  • Tags
    Fractions
In summary: No, but 3 does. Divide both numerator and denominator by 3. In summary, 0.272727 = 272727/1000000 = 272727/2(500000)= 9/33= 3/11.
  • #1
Cliff Hanley
90
2
I came across the following question on the BBC website;

Convert 0.272727 to a fraction. It was a multiple choice question so I could test each possible answer by dividing the numerator by the denominator until I got the right one. But it made me wonder how I could have answered it had it not been multiple choice. I could have got as far as 272,727/1,000,000 but then how would I know how to reduce that? I know to look for common factors but would struggle with such a large number.

There was another example also; convert 0.6121212 to a fraction.
 
Mathematics news on Phys.org
  • #2
0.272727 = 27/100 + 27/10000 + 27/1000000 = 27*( ... )
 
  • #3
Cliff Hanley said:
I came across the following question on the BBC website;

Convert 0.272727 to a fraction. It was a multiple choice question so I could test each possible answer by dividing the numerator by the denominator until I got the right one. But it made me wonder how I could have answered it had it not been multiple choice. I could have got as far as 272,727/1,000,000 but then how would I know how to reduce that? I know to look for common factors but would struggle with such a large number.

There was another example also; convert 0.6121212 to a fraction.

Suppose you take a two-digit number: 27 for example. Let's look at 2700/99. For every 100, 99 goes into it once and leaves a remainder of 1. So, when you divide 2700 by 99, you get 27 plus a remainder of 27:

2700 = (27 × 99) + 27

Therefore:

2700/99 = 27.272727...

and:

27/99 = 0.272727...

It's the same for any two digit number:

35/99 = 0.353535...

06/99 = 0.060606...

For 1-digit numbers you have:
1/9 = 0.11111...
2/9 = 0.22222...
3/9 = 0.33333...

Etc.

And for 3-digit numbers you have:

001/999 = 0.001001001...

123/999 = 0.123123123

etc.
 
  • #4
Was the problem to convert .272727 to a fraction or was it written as .272727...; i.e., with the dots, indicating that the same pattern repeats infinitely?
 
  • #5
Equivalently, if we let x= 0.27272727... then 100x= 27.272727... Now subtracting 100x- x leaves the integer 27 (the fact that the "27" part of the decimal is infinitely repeating means that we will always have the "27"s continuing after the decimal point so they all cancel). That is, 100x- x= 99x= 27 so x= 27/99.

Every fraction is equivalent to a repeating decimal.

(We count 1/2= 0.5 as 0.500000... with the "0" repeating. Every fraction with denominator having only "2"s and "5"s as factors of the denominator is such a "terminating" decimal.)
 
  • #6
Cliff Hanley said:
Convert 0.272727 to a fraction.

HallsofIvy said:
Equivalently, if we let x= 0.27272727...
These are two different and unrelated problems. Possibly the OP is unaware of the difference between .272727 and .272727...

We should hold off on further responses until the OP returns to clarify what he is asking.
 
  • #7
Thank you. I completely missed that!
 
  • #8
Cliff Hanley said:
I came across the following question on the BBC website;

Convert 0.272727 to a fraction. It was a multiple choice question so I could test each possible answer by dividing the numerator by the denominator until I got the right one. But it made me wonder how I could have answered it had it not been multiple choice. I could have got as far as 272,727/1,000,000 but then how would I know how to reduce that? I know to look for common factors but would struggle with such a large number.

There was another example also; convert 0.6121212 to a fraction.
Surely you know that 1,000,000 is a power of 10, [itex]10^6[/itex]? And that 10= 2*5? So the denominator has factors of only 2 and 5. Do 2 or 5 divide 272727?
 

FAQ: Converting decimals to fractions

1. What is the easiest way to convert a decimal to a fraction?

The easiest way to convert a decimal to a fraction is to think of the decimal as a fraction with 1 as the denominator. Then, count the number of decimal places and put that number in the denominator, and put the digits to the right of the decimal point in the numerator. Finally, simplify the fraction if possible.

2. How do I convert a decimal to a fraction without a calculator?

To convert a decimal to a fraction without a calculator, follow these steps: 1) Write the decimal as a fraction with 1 as the denominator. 2) Multiply both the numerator and denominator by 10 (or 100, 1000, etc.) until the decimal is removed. 3) Simplify the resulting fraction if possible.

3. Can all decimals be converted to fractions?

Yes, all decimals can be converted to fractions. This is because a decimal is simply another way of representing a fraction. However, some decimals may result in fractions with large denominators, making them more difficult to work with.

4. How do I convert repeating decimals to fractions?

To convert a repeating decimal to a fraction, first write the decimal as a fraction with 1 as the denominator. Then, multiply both the numerator and denominator by a number that will eliminate the repeating pattern. Finally, simplify the resulting fraction if possible.

5. Can I convert a fraction to a decimal?

Yes, fractions can be converted to decimals. To do this, divide the numerator by the denominator. The resulting decimal may either terminate or repeat. To convert a fraction to a decimal without a calculator, follow the steps for converting a decimal to a fraction without a calculator.

Similar threads

Back
Top