The decimal numeral system which is also known as the base-ten positional numeral system refers to a standard system that is used for the purposes of denoting integer as well as non-integer numbers. It may also be referred to as denary. Decimal notation is the term that is used to describe the manner of denoting the numbers that are in the decimal system.
Fraction, on the other hand, is a term that is used to refer to any number of parts that are equal or parts that make up a whole. The representation of a fraction is done using the numerator and the denominator. The numerator is the number that is placed above the line while the denominator is that which is placed just below the line.
The conversion of decimals to fractions follows a series of steps as discussed below:
Step 1. Start by dividing the decimal by one. Write the decimal number as the numerator and 1 as the denominator. This can be expressed as decimal ∕ 1.
Step 2. Multiply both the numerator and the denominator by ten for each number that falls after the decimal point. If two numbers fall after the decimal point like 1.12, then, we multiply by 100. In case three numbers fall after the decimal point like 3.615, then, we multiply by 1,000.
Step 3. Reduce the fraction. It can also be referred to as simplifying the fraction.
Example: assuming that you are told to convert the decimal 0.50 into a fraction, here is what you do,
Solution,
Step 1. Write down 0.50 divided by one. This can be expressed as 0.50 ∕ 1.
Step 2. Multiply both the numerator and the denominator by 100. This is so due to the fact that there are only two digits that come after the decimal point. Therefore \(\frac{0.50 \times 100}{1 \times 100}\). The result is 50 ∕ 100.
Step 3. Reduce the fraction. This fraction can be reduced by dividing with the common divisor 50. 50 ÷ 50= 1 and 100 ÷ 50 = 2. The final answer, therefore, is ½. It is important to note that 50 ∕ 100 is referred to as a decimal fraction while ½ is referred to as the common fraction.
Example 2. Convert 0.750 to a fraction.
Solution,
Step 1. 0.750 ∕ 1
Step 2. \(\frac{0.750 \times 1000}{1 \times 1000}\)The result will be 750 ∕ 1000.
Step 3. Reduce the fraction. The common divisor in this case, for both the numerator and the denominator, is 250. Divide both numbers by 250. 750 ÷ 250 = 3 and 1000 ÷ 250 = 4. The final result, therefore, is ¾.
Example 3. Convert 1.25 to a fraction.
Solution,
Step 1. Just work on 0.25 and put 1 aside. Write down 0.25 divided by one. This can be expressed as 0.25 ∕ 1.
Step 2. Multiply both the numerator and the denominator by 100. This is because there are two digits that come after the decimal point. In this case, we get 25 ∕ 100.
Step 3. Reduce the fraction. Divide both the numerator and the denominator by the common divisor 25. 25 ÷ 25 = 1 and 100 ÷ 25 = 4. Therefore, the answer is ¼. Bring back the 1 to make it a mixed fraction. Therefore, the final answer is 1 ¼.
