ESTIMATING MULTIPLICATION WITH DECIMALS

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 48 x 29, we have

48 ----> 50 and 29 ---->30

In 52 x 31, we have

52 ----> 50 and 31 ---->30

Solved Problems

Problem 1 :

Estimate the product of :

28.3 x 3.2

Solution :

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

28.3  -----> 30

3.2 -----> 3

Now, the above product will become

30 x 3

Then, the estimated product is

=  3 x 3  =  9 -----> 90

Problem 2 :

Estimate the product of :

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 product will become

30 x 4

Then, the estimated product is

=  3 x 4  =  12 -----> 120

Problem 3 :

Estimate the product of :

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 product will become

70 x 6

Then, the estimated product is

=  7 x 6  =  42  -----> 420

Problem 4 :

Estimate the product of :

328 x 42

Solution :

This is bit different case.

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

328  -----> 300

42 -----> 40

But both the numbers are decreased. (Because 328 is close to 300 and 42 is close to 40)

Now, the estimated product is

=  3 x 4  =  12 -----> 12000

But the exact product is 13776.

Here, there is bit higher difference between the exact product and estimation.

So, we can round the given numbers as given below.

328 -----> 350

42 -----> 40

Now, the product will become

350 x 40

Then, the estimate of the product is

=  35 x 4  =  140 -----> 14000

Problem 5 :

Estimate the product of :

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 product will become

400 x 60

Then, the estimated product

=  4 x 6  =  24 -----> 24000

Problem 6 :

Estimate the product of :

5283 x 78

Solution :

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

5283  -----> 5000

78 -----> 80

Now, the above product will become

5000 x 80

Then the estimated product is

=  5 x 8  =  40 -----> 400000

Problem 7 :

Estimate the product of :

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 product will become

7000 x 70

Then, the estimated product is

=  7 x 7  =  49 -----> 490000

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