Notes On Multiplication and Division on Decimals - CBSE Class 7 Maths

Multiplication of decimals

Steps to multiply a whole number by a decimal number:
Step 1: Ignore the decimals and multiply the two numbers.
Step 2: Count the number of digits to the right of decimal point in the original decimal number.
Step 3: Insert the decimal in the answer by the same count from right to left.
e.g. (i)   3 × 0.2 = 0.6  (ii) 3 × 0.4 = 1.2

Steps to multiply a decimal number by a decimal number:
Step 1: Ignore the decimals and multiply the two numbers.
Step 2: Count the number of digits to the right of decimal point in both the decimal numbers
Step 3: Add the number of digits counted and insert the decimal in the answer by the same count from right to left.
e.g. (i) 0.2 × 0.7 = 0.14 (ii) 0.9 × 0.02 = 0.018

Multiplication of a decimal number by 10, 100 or 1000:

  • For multiplying a decimal number by 10, retain the original number and shift the decimal to the right by one place
  • For multiplying a decimal number by 100, retain the original number and shift the decimal to the right by two places
  • For multiplying a decimal number by 1000, retain the original number and shift the decimal to the right by three places


Division of decimals

Steps to divide a decimal number by a whole number:
Step 1: Convert the decimal number into a fraction.
Step 2: Find the reciprocal of the divisor.
Step 3: Multiply the fraction by the reciprocal.
e.g. 0.14 ÷ 314 100 × 1 3 14 300   

Steps to divide a decimal number by another decimal number:
Step 1: Convert both the decimal numbers into fractions.
Step 2: Find the reciprocal of the divisor.
Step 3: Multiply the fraction by the reciprocal.
e.g. 0.45 ÷ 0.15 = 45 100 ÷ 15 100 = 45 100 × 100 15 = 3

Summary

Multiplication of decimals

Steps to multiply a whole number by a decimal number:
Step 1: Ignore the decimals and multiply the two numbers.
Step 2: Count the number of digits to the right of decimal point in the original decimal number.
Step 3: Insert the decimal in the answer by the same count from right to left.
e.g. (i)   3 × 0.2 = 0.6  (ii) 3 × 0.4 = 1.2

Steps to multiply a decimal number by a decimal number:
Step 1: Ignore the decimals and multiply the two numbers.
Step 2: Count the number of digits to the right of decimal point in both the decimal numbers
Step 3: Add the number of digits counted and insert the decimal in the answer by the same count from right to left.
e.g. (i) 0.2 × 0.7 = 0.14 (ii) 0.9 × 0.02 = 0.018

Multiplication of a decimal number by 10, 100 or 1000:

  • For multiplying a decimal number by 10, retain the original number and shift the decimal to the right by one place
  • For multiplying a decimal number by 100, retain the original number and shift the decimal to the right by two places
  • For multiplying a decimal number by 1000, retain the original number and shift the decimal to the right by three places


Division of decimals

Steps to divide a decimal number by a whole number:
Step 1: Convert the decimal number into a fraction.
Step 2: Find the reciprocal of the divisor.
Step 3: Multiply the fraction by the reciprocal.
e.g. 0.14 ÷ 314 100 × 1 3 14 300   

Steps to divide a decimal number by another decimal number:
Step 1: Convert both the decimal numbers into fractions.
Step 2: Find the reciprocal of the divisor.
Step 3: Multiply the fraction by the reciprocal.
e.g. 0.45 ÷ 0.15 = 45 100 ÷ 15 100 = 45 100 × 100 15 = 3

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