Common problems in math is converting decimals to fractions. Here are the basic ways used for conversions.

Arjun Kulkarni
May 10, 2019

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Converting fractions to decimals is a rather simple procedure, simply a matter of dividing the numerator by the denominator. On the other hand, converting decimals to fractions might seem to be a bit tricky.

Basic numerical conversions are not all that tough. Let me explain this with the help of an example.

Suppose you have the number 8.78, and you want to convert it.

★ First, count the number of digits after the decimal point. In this case, we have two digits.

★ First, count the number of digits after the decimal point. In this case, we have two digits.

★ You multiply and divide the given number with another number. The multiplier is always 1, followed by as many zeros as the number of digits after the decimal point. So, since the given number has 2 digits after the decimal point, it will be multiplied and divided by 1, followed by 2 zeros, i.e., 100.

★ Then you simply have to reduce the resulting fraction to its simplest form by dividing the numerator by the common multiples which it shares with the denominator.

= 8.78 × 100÷100

= 878÷100

= 439÷50

If you want to convert this into a mixed fraction, divide 439 by 50. The quotient will be the main number, the remainder will be the numerator, and the dividend will be the denominator. Hence, the answer is, 8 39÷50.

Let us take an example about converting repeating decimals to fractions. Now, a number with repeating decimals does not terminate. So what do you do in this case? For example, let's take the number 0.2989898.

★ The first step is to find out how many digits repeat. In this case, the number of digits repeating is 2. And the repeating digits come after '2'. So that makes it total of 3 digits. Hence, you multiply the number with 1 and three zeros, i.e., 1000.

★ Hence, you have 298.9898. Now, divide only the integer part by 1 less than what you multiplied the original number with, i.e., 298÷999. And this is your answer

multiply

= 0.136136136 × 1000 (3 repeating digits)

= 136.136136136

divide integer to get the answer

= 136÷999 (one less than the multiplier)

Conversion in Microsoft Excel is a slightly different process. Actually, you can't really convert a decimal to a numerator-denominator fraction in Excel. What Excel can do for you is change the base of the number.

Suppose, you want to know what is 6.5 hours, it is not 6 hours 50 minutes, because the base here is 60. So what you need to do is, go to the functions wizard and pick the 'DOLLARFR' option.

In the decimal dollar field, you put 6.5, and in the fraction field, you put 60 (60 minutes to an hour). And you get the answer 6.3. This means that 6.5 hours is actually 6 hours 30 minutes.