Converting an ordinary fraction to a decimal

In this publication, we will consider how an ordinary (simple) fraction can be converted into a decimal (finite and infinite). We will also analyze the solution of examples for a better understanding of the material presented.

Converting a fraction to a decimal

To convert a fraction to a decimal, you can use one of the two methods below:

1 method

Both the numerator and the denominator are multiplied by the same number. In this case, the number must be such that the denominator of the new fraction is divisible by 10, 100, 1000, 10000, etc.

Condition: this method is suitable only for such fractions, the denominator of which is decomposed into simple factors of 2 or 5 (can be repeated). The result will be a final decimal. In other cases, you need to use Method 2described below.

Example 1:

Solution

Example 2:

Solution

The given fraction cannot be converted to a final decimal because the denominator 12 is decomposed into prime factors: 2, 2 and 3. And this contradicts the condition mentioned above.

2 method

This method is much more popular than the first. The algorithm of actions is as follows:

1. First, we divide the numerator by the denominator as usual (in a column).
2. As soon as we encounter the fact that the remainder of the division is no longer divisible by the divisor, then:
   • in private we put a comma;
   • add zero to the remainder and continue dividing the resulting number by the divisor, writing the result to the right of the decimal point. And so on, until we get a remainder equal to zero (for finite decimals) or the required number of digits after the decimal point (for infinite fractions).
   • Note: If the numerator is greater than the denominator, then the decimal fraction will be greater than one, if less, the integer part of the decimal fraction is equal to zero (therefore, in private we write 0, put a comma and continue to perform the division, writing the resulting numbers in the fractional part).

IMPORTANT: A mixed fraction must be represented as an improper fraction before being converted to a decimal.

Example 1:

Solution

Example 2:

Solution