ESTIMATE PRODUCTS

When we want to do the multiplications of  

"Three digit number x One digit number"

"Three digit number" x Two digit number"

"Decimal number x Decimal number"

we have to calculate step by step.

Sometimes we may have to estimate the above products without step by step calculation.

Even though estimation is just approximation of the exact answer, we can get quickly.

Rule to be Followed in Estimating the Products

When we estimate multiplication with decimal, we have to follow the rule given below as much as possible.

If one number is increased to round off, then decrease the other number (if it is needed to round off).

Sometimes we may have to either increase both the numbers or decrease both the numbers to round off.

Examples : 

In 59 x 31, we have

59 ----> 60 and 31 ----> 30

In 62 x 41, we have

62 ----> 60 and 41 ----> 40

Examples

Example 1 :

Estimate :

38 x 42

Solution :

In the above product, the numbers can be rounded as given below.

38 -----> 40

42 -----> 40

Now, the above multiplication will become

40 x 40

Then, the estimated product is

=  4 x 4  =  40 -----> 1600

Example 2 :

Estimate :

203 x 96

Solution :

In the above product, the numbers can be rounded as given below.

203 -----> 200

96 -----> 100

Now, the above multiplication will become

200 x 100

Then, the estimated product is

=  2 x 1  =  2 -----> 20000

Example 3 :

Estimate :

29.3 x 4.1

Solution :

In the above product, the numbers can be rounded as given below.

29.3  -----> 30

4.1 -----> 4

Now, the above multiplication will become

40 x 4

Then, the estimated product is

=  4 x 4  =  16 -----> 160

Example 4 :

Estimate :

34.3 x 3.5

Solution :

In the above product, the numbers can be rounded as given below.

34.3  -----> 30

3.5 -----> 4

Now, the above multiplication will become

30 x 4

Then, the estimated product is

=  3 x 4  =  12 -----> 120

Example 5 :

Estimate :

74.8 x 5.7

Solution :

In the above product, the numbers can be rounded as given below.

74.8  -----> 70

5.7 -----> 6

Now, the above multiplication will become

70 x 6

Then, the estimated product is

=  7 x 6  =  42  -----> 420

Example 6 :

Estimate :

428.5 x 57.3

Solution :

In the above product, the numbers can be rounded as given below.

428.5  -----> 400

57.3 -----> 60

Now, the above multiplication will become

400 x 60

Then, the estimated product

=  4 x 6  =  24 -----> 24000

Example 7 :

Estimate :

5283 x 78

Solution :

In the above product, the numbers can be rounded as given below.

5283  -----> 5000

78 -----> 80

Now, the above multiplication will become

5000 x 80

Then the estimated product is

=  5 x 8  =  40 -----> 400000

Example 8 :

Estimate :

6523.56 x 73.569

Solution :

In the above product, the numbers can be rounded as given below.

6523.56  -----> 7000

73.569 -----> 70

Now, the above multiplication will become

7000 x 70

Then, the estimated product is

=  7 x 7  =  49 -----> 490000

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