DEFINITION OF A DECIMAL FRACTION – MINDSPARK

DECIMAL FRACTION

Fraction is made up of two parts namely numerator and denominator. When a fraction or a mixed number has the denominator 10 or a power of 10 such as 10, 100, 1000, 1000, etc., which is usually expressed by using the decimal point, it is called a decimal fraction. Writing fraction in terms of decimals makes it easier to carry mathematical operations as well as compare the values. It is difficult to compare fractions if the denominators are different. Also, it is easier to convert fractions that have denominators as a power of 10 into decimals. 

Examples of decimal fractions are:

5/10 = 0.5 (can be read as five-tenth)

5/100 = 0.05 (can be read as five-hundredth)

5/1000 = 0.005 ( can be read as five-thousandth)

54/100 = 0.54 (can be read as fifty-fourth hundredths)

63/1000 = 0.063 (can be read as sixty-third thousandth)

OPERATIONS ON DECIMAL FRACTIONS

• Addition 

The numbers in decimals are placed keeping in mind that the decimals are placed such that they are below one another and the numbers are added normally just like in the case of whole numbers. For example, add 0.00023 and 0.00569:

• Subtraction

Subtraction is done just like addition. The only thing to be mindful of is the position of the decimals. The decimals in the case of two numbers must be below one another and then carry on the operation of subtraction. For example, subtract 0.00526 from 0.08955:

• Multiplication

We can multiply by converting them into fractions again or in decimal form as well.

Let us consider different cases. The first case is when a number is multiplied by a multiple of 10. 

For example, if we have to multiply the number 5.234 by 100 then we shift the decimal to the right by the number of zeroes in the multiple of 10. Here, we have 2 zeroes so we shift the decimal places by 2 places so the answer to 5.234 x 100 = 523.4.

Now, if we have to multiply decimal fractions. Let us say we have to multiply 0.3 x 0.2. we can convert them into fractions like 3/10 and 2/10. We get, \frac{3}{10} \times \frac{2}{10}=\frac{6}{100}=0.06.

Or we can multiply them directly as well. Multiply the numbers without considering the decimal points. Here 3 x 2 = 6 and then place the decimals to the left of the number as much as is the sum of the number of decimal places. Here the sum of decimal places is 1 + 1 = 2 so the answer is 0.06.

We can consider another case, 0.5 x 0.006.

Now, multiply 5 and 6 we get 30. We will sum the number of decimal places here:  1 + 3 = 4 so we will place the decimal 4 places to the left of the number 30. We will get the answer as 0.5 x 0.006 = 0.0030.

• Division

It is easy to divide a number by 10 or multiples of 10. Say if we have to divide the decimal fraction 56.258 by 100. We will shift the decimal places by the number of zeroes in the multiple of 10. So here, there are two zeroes so we will shift the decimal places by two places. 

We get, 56.258/100 = 0.56258.

Also, when we have to divide one decimal fraction by another decimal fraction, we can either normally divide the numbers and then place the decimals after counting the number of decimals in the dividend and divisor and finding their difference.

Say, if we have to divide 0.0066 by 0.11 When we divide 66 by 11 we get 6. Now, place the number of decimals 4 places to the left. We get 0.0066 x 0.11 = 0.06 (since 4 places to the left of the dividend – 2 places to the left of the divisor).

Or when we divide 0.0066/0.11, we can multiply the numerator and denominator by such a multiple of 10 such that the denominator becomes a whole number.

(0.0066 x 100) / (0.11 x 100) = 0.66/11 = 0.06