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

Practice 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

Apart from the stuff given above, if you need any other stuff, please use our google custom search here. 

You can also visit the following web pages on different stuff in math. 

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation 

Word problems on unit price

Word problems on unit rate 

Word problems on comparing rates

Converting customary units word problems 

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles 

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems 

Profit and loss word problems 

Markup and markdown word problems 

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed 

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS 

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6