CBSE Class 7 Mathematics – 3. Decimals (Notes)

Revision Notes on Decimals

Learning Goal

Decimals

1. Decimal (Fractions whose denominator is exponent of 10. Ie. 10, 100, 1000 etc.)
2. Part of decimal (Whole part & decimal part)
3. Type of decimal (Like and Unlike decimal)
4. Multiplication of Decimal Numbers

(a) How to multiply a decimal number with a whole number?

(b) How to multiply Decimal numbers by 10,100 and 1000?

(c) How to multiply a decimal number by another decimal number?

5. Division of Decimal Numbers

(a) How to divide a decimal number with a whole number?

(b) How to divide Decimal numbers by 10,100 and 1000?

(c) How to divide a decimal number by another decimal number?

Decimal Numbers

Fractions whose denominators are exponent of 10 are called Decimal Fractions. OR

Fractions whose denominators are 10, 100, 1000 etc are called Decimal Fractions.

Part of Decimal Numbers

Multiplication of Decimal Numbers

1. How to multiply a decimal number with a whole number?

Multiply them as normal numbers but the decimal place will remain the same as it was in the original decimal number.

Example

35 × 3.45 = 120.75

Here we have multiplied the number 35 with 345 as normal whole numbers and we put the decimal at the same place from the right as it was in 3.45.

2. How to multiply Decimal numbers by 10,100 and 1000?

a. If we have to multiply a decimal number by 10 then we will transfer the decimal point to the right by one place.

Example

5.37 × 10 = 53.7

b. If we have to multiply a decimal number by 100 then we will transfer the decimal point to the right by two places.

Example

5.37 × 100 = 537

c. If we have to multiply a decimal number by 1000 then we will transfer the decimal point to the right by three places.

Example

5.37 × 1000 = 5370

3. How to multiply a decimal number by another decimal number?

Multiply them as the normal whole numbers then put the decimal at such place so that the number of decimal place in the product is equal to the sum of the decimal places in the given decimal numbers.

Example

Division of Decimal Numbers

1. How to divide a decimal number with a whole number?

Divide them as normal number but the decimal place will remain the same as it was in the original decimal number.

Example

12.96 ÷ 4 = 3.24

Here we divide the number 1296 with 4 as normal whole numbers and we put the decimal at the same place from the right as it was in 12.96.

2. How to divide Decimal numbers by 10,100 and 1000?

a. If we have to divide a decimal number by 10 then we will transfer the decimal point to the left by one place.

Example

5.37 ÷ 10 = 0.537

b. If we have to divide a decimal number by 100 then we will transfer the decimal point to the left by two places.

Example

253.37 × 100 = 2.5337

c. If we have to divide a decimal number by 1000 then we will transfer the decimal point to the left by three places.

Example

255.37 × 1000 = 0.25537

3. How to divide a decimal number by another decimal number?

To divide a decimal number with another decimal number

First, we have to convert the denominator as the whole number by multiplying both the numerator and denominator by 10, 100 etc

Now we can divide them as we had done before.

Example

Here we had converted denominator 2.4 in the whole number by multiplying by 10. Then divide it as usual.