MULTIPLYING DECIMALS - METHODS OF MULTIPLYING WITH SOLVED EXAMPLES AND EXERCISE

Please study
Multiplication before Multiplying Decimals

if you have not already done so.

The knowledge of the method of Multiplying
whole numbers with vertical presentation
is a prerequisite here. Once you master Multiplying
whole numbers, the methods described here,
are easy to follow.

But remember that, simple things need perfection
and perfection is not a simple thing.

Study the Examples and solve the problems
given in exercise and check with the Answers.

Multiplying Decimals by 10, 100, 1000 etc.

When a decimal number is multiplied by 10, the
decimal point moves to the right by one place.

When a decimal number is multiplied by 100, the
decimal point moves to the right by two places.

When a decimal number is multiplied by 1000, the
decimal point moves to the right by three places.

and so on.

Thus, we observe :

When a decimal number is multiplied by numbers like 10,
100, 1000...., the decimal point in the given decimal
number moves as many places to the right as the number of
zeros in the multiplier. If there are not enough (adequate)
places on the right side, we keep '0' s in those places.

Examples :

1. 9.62 x 10 = 96.2 ( decimal point shifted 1 place to the right )
2. 1.13 x 10000 = 11300 ( decimal point shifted 4 places to the right )
3. 6.9732 x 1000 = 6973.2 ( decimal point shifted 3 places to the right )
4. 0.01 x 100 = 1 ( decimal point shifted 2 places to the right )
5. 0.999 x 100000 = 99900 ( decimal point shifted 5 places to the right )

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Multiplying Decimals by a whole number

Step 1 :
Multiply the given numbers ignoring decimal point.

Step 2 :
Count the number of places after decimal point
in the decimal. Let it be 'n'.

Step 3 :
In the product obtained in step 1, count 'n' (value
in step 2) number of places to the left from the
right end and keep decimal point to obtain product.

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Example on Multiplying Decimal by a whole number

Find 9.182 x 43

Solution :
We, first find 9182 x 43 (i.e. by removing decimal point)

            9182
              43
          ------           2  
           27546        3  
          36728
          ------
          394826
          ------

Thus 9182 x 43 = 394826

If you want explanation for this, goto

Multiplication

and study the explanation given to Example 17, there.

Now,decimal point will be placed 3 places
(as in the multiplying decimal) from right.

∴ 9.182 x 43 = 394.826 Ans.

Multiplying Decimal by decimal

Step 1 :
Multiply the given numbers ignoring decimal points.

Step 2 :
Count the number of places after decimal point
in each of the decimals. Let they be 'n₁' and 'n₂'.
Add 'n₁' and 'n₂' to get 'n'.

Step 3 :
In the product obtained in step 1, count 'n' (value
in step 2) number of places to the left from the
right end and keep decimal point to obtain product.

Example on Multiplying Decimal by decimal

Find 14.32 x 2.513

Solution :
We, first find 1432 x 2513 (i.e. by removing decimal points)

              1432
              2513
          ---------              1  
             4296             
            1432              1  1 2
           7160
          2864
          ---------
          3598616
          ---------

Thus 1432 x 2513 = 3598616

If you want explanation for this, goto

Multiplication

and study the explanation given to Example 19, there.

Now,decimal point will be placed 5 places
(as in the multiplying decimals 2 + 3 = 5) from right.

∴ 14.32 x 2.513 = 35.98616 Ans.

Exercise

Find the products

1.  
   1. 39.641 x 100
   2. 34.754 x 100000
   3. 15.05 x 1000
   4. 0.08 x 10
   5. 0.7 x 10000
2.  
   1. 63.47 x 8
   2. 2.375 x 148
3.  
   1. 0.235 x 0.137
   2. 0.075 x 0.009

For Answers, see at the bottom of the page.

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Answers to Exercise

1.  
   1. 3964.1
   2. 3475400
   3. 15050
   4. 0.8
   5. 7000
2.  
   1. 507.76
   2. 351.5
3.  
   1. 0.032195
   2. 0.000675