ESTIMATING MULTIPLICATION WITH DECIMALS

About "Estimating multiplication with decimals"

"Estimating multiplication with decimals"  is the stuff much needed to the children who study math in schools and also for many people in their day to day life.

Students are able to remember exact answers for the questions  of

"Single digit number x Single digit number"

Example:

6 x 7 = 42                               8 x 9 = 72                             4 x 9 = 36

When they have multiplications of  

"Two digit number x Single digit number"

They are able to get exact answer by using the shortcut given below.

But, when students 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"

they have to calculate step by step. Sometimes students would be asked 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 are trying to do "estimating 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

How to estimate  the product of two number ?

When we do "estimating multiplication with decimals", we have to round the given numbers to the nearest compatible numbers.

Example 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 30x3

Then the estimated product = 3x3 = 9 ===> 90

Example 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 30x4

Then the estimated product = 3x4 = 12 ===> 120

Example 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 70x6

Then the estimated product = 7x6 = 42 ===> 420

Example 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 ===> 300 x 40 = 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 = 35x4 = 140 ===>14000

Example 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 = 4x 6 = 24 ===> 24000

Example 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 = 5x8 = 40 ===> 400000

Example 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 = 7x7 = 49 ===> 490000

We hope the student now understand the concept "Estimate Products"

Click the below links to know more about "Estimating multiplication with decimals"

1. Estimate the products

2. Estimate the product of decimals