Multiplication of Decimal Numbers

In multiplication of decimal numbers we will learn how to find the product of a decimal and a whole number.

The rules of multiplying decimals are:

(i) Take the two numbers as whole numbers (remove the decimal) and multiply.

(ii) In the product, place the decimal point after leaving digits equal to the total number of decimal places in both numbers.

(iii) Counting decimal point must always be done from the units place of the product.

A. Multiplication of a Decimal by a Whole Number

Let us follow some of the examples on multiplication of a decimal fraction by a whole number.

To multiply a decimal number by a whole number, we first multiply the two numbers ignoring the decimal points and then place the decimal point in the product to have the same number of decimal places as in the given decimal number.

1. Find 43.5 × 4.

First we will perform the multiplication ignoring decimal point.

Now place the decimal point in the product to get as many decimal places in the product as there are in the multiplicant. And, here the multiplicant contains one decimal place, so the product must contain one decimal place.

Thus, 43.5 × 4 = 174.0 = 174

2. Find 91.32 × 83.

First we will perform the multiplication ignoring decimal point.

Here the multiplicant contains two decimal places, so the product must contain two decimal places.

Thus, 91.32 × 83 = 7579.56


3. Find the product of 49.6 × 14

First perform multiplication ignoring decimal point as we do in whole numbers.

Here the multiplicant contains one decimal place, so the product must contain one decimal place.

Thus, 49.6 × 14 = 694.4

4. Multiply 19.67 by 6.

Solution:

19.67 × 6

In 19.67, there are 2 decimal places after the decimal point.

Place the decimal point to have two decimal places after the point.

B. Multiplying Two Decimals

In such a case also, we multiply the decimals as usual without any consideration of the decimal point. The product will have the same number of decimal places as the multiplicand and multiplier have together.

Let us consider some examples.

1. Multiply 24.16 by 2.3.

Solution:

Step I: Arrange the decimals in columns.

Step II: Multiply the numbers ignoring the decimal point.

            2416 × 3  =      7248

            2416 × 20 = + 48320

                                   55568

Step III: Count the number of decimal places in the multiplicand and multiplier and add them. Here, it is 2 + 1 = 3

Step IV: Count 3 digits from the extreme right of the product and insert the decimal point 55568 → 55.568

Multiply 24.16 by 2.3.

      24.16 → Decimal point after two digits from the right

      × 2.3 → Decimal point after one digit from the right

      7248

 + 48320

   55.568  → Decimal point after three (2 + 1) digits from the right

Answer: 55.568

2. Multiply 125.32 by 3.23.

Solution:

Step I: Arrange the decimals in columns.

Step II: Multiply the numbers ignoring the decimal point.

            12532 × 3      =        37596

            12532 × 20    =       250640

            12532 × 300  =  + 3759600

                                        4047836

Step III: Count the number of decimal places in the multiplicand and multiplier and add them. Here, it is 2 + 2 = 4

Step IV: Count 4 digits from the extreme right of the product and insert the decimal point 4047836 → 404.7836

Multiply 125.32 by 3.23.

        125.32 → Decimal point after two digits from the right

        × 3.23 → Decimal point after two digits from the right

        37596

      250640

 + 3759600

   404.7836  → Decimal point after four (2 + 2) digits from the right

Answer: 404.7836

● Decimal.

• Tenth Place in Decimals
  
• Hundredths Place in Decimals
• Thousandths Place in Decimals
  
• Whole Numbers and Decimals
  
• Decimal Place Value Chart.
• Expanded form of Decimal Fractions
• Like Decimal Fractions.
• Unlike Decimal Fraction.
• Equivalent Decimal Fractions.
• Changing Unlike to Like Decimal Fractions.
• Ordering Decimals
• Comparison of Decimal Fractions.
• Conversion of a Decimal Fraction into a Fractional Number.
• Conversion of Fractions to Decimals Numbers.
• Addition of Decimal Fractions.
• Problems on Addition of Decimal Fractions
• Subtraction of Decimal Fractions.
• Problems on Subtraction of Decimal Fractions
• Multiplication of a Decimal Numbers.
• Multiplication of a Decimal by 10, 100, 1000
• Multiplication of a Decimal by a Decimal.
• Properties of Multiplication of Decimal Numbers.
• Problems on Multiplication of Decimal Fractions
• Division of a Decimal by a Whole Number.
• Division of Decimal Fractions
• Division of Decimal Fractions by Multiples.
• Division of a Decimal by a Decimal.
• Division of a whole number by a Decimal.
• Properties of Division of Decimal Numbers
• Problems on Division of Decimal Fractions
• Conversion of fraction to Decimal Fraction.
• Simplification in Decimals.
• Word Problems on Decimal.

5th Grade Numbers Page

5th Grade Math Problems

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