**Important Concepts and Formulas on Decimals**

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.