Class 7 Chapter 3: Decimals

# Class 7 Chapter 3: Decimals

Important Concepts and Formulas on Decimals

1.      Decimals are fractions with denominators 10, 100, 1000, 10000 and so on.

2.      When we write decimal fractions without denominators using decimal point, they are called decimal numbers. For example, 34/10 can be written as 3.4.

3.      A decimal number has two parts: a whole number part (integral part) and a decimal part.

4.      The number of digits in the decimal part of a decimal number determines the decimal places of that number.

5.      Decimals having the same number of decimal places are called like decimals, otherwise they are unlike decimals.

6.      Unlike decimals can be converted into like decimals by adding required number of zeros at the end of the decimal part.

7.      To compare two decimal numbers, first we compare the whole number part. If they are equal then the tenth part is compared. If they are also equal, then the subsequent parts are compared.

8.      Every decimal number can be converted as a fraction and vice versa.

9.      To add or subtract decimals, convert them into like decimals. Then add or subtract them like whole numbers by keeping decimal points of the given decimals in the same column.

10. To multiply a decimal number by 10, 100 or 1000, shift the decimal point to the right by as many places as there are zeros after 1. For example, 681.45 × 10 = 6814.5; 681.45 × 100 = 68145; 681.45 × 1000 = 681450.

11. To divide a decimal number by 10, 100 or 1000, shift the decimal point to the left by as many places as there are zeros after 1. For example, 681.45 ÷ 10 = 68.145; 681.45 ÷ 100 = 6.8145; 681.45 ÷ 1000 = 0.68145.

12. While converting lower units of length and weight to their higher units, we use decimals. For example, 45 cm = 0.45 m and 18 g = 0.018 kg.

13. To divide a decimal by another decimal, move the decimal point in the divisor and dividend by the same number of places to make the divisor a whole number. Divide and put the decimal point in the quotient directly above the decimal point in the dividend. For example, 27.419/0.23 = 2741.9/23.