ESTIMATE TO CHECK REASONABLENESS

Suppose we multiply two decimals, say 1.98 and 2.89. In case, we are not sure whether the answer we got is correct or wrong, we can use estimation to check that our answer is reasonable.

Let us look at some examples to check reasonableness.  

Example 1 :

Delia bought 3.8 pounds of peppers. The peppers cost $1.99 per pound. What was the total cost of Delia’s peppers ?

Solution :

The peppers cost $1.99 per pound.

To find the cost of 3.8 pounds, we have to multiply 1.99 and 3.8 as given below. 

If we round the answer 7.562 to the nearest hundredth, we get 7.56

So, the cost of 3.8 pounds of peppers is $7.56.

Now, let us estimate to check whether our answer is reasonable.

Round 1.99 to the nearest whole number.

That is, 2

Round 3.8 to the nearest whole number.

That is, 4 

Multiply the whole numbers 2 and 4.

That is,

2 x 4  =  8

The answer is reasonable. Because 8 is close to 7.56.

Example 2 :

Blades of grass grow 3.75 inches per month. If the grass continues to grow at this rate, how much will the grass grow in 6.25 months ?

Solution :

Blades of grass in one month  =  3.75 inches.

To find the amount grass grown in 6.25 months, we have to multiply 3.75 and 6.25 as given below. 

So, the grass will grow 23.4375 inches in 6.25 months.

Now, let us estimate to check whether our answer is reasonable.

Round 3.75 to the nearest whole number.

That is, 4

Round 6.25 to the nearest whole number.

That is, 6 

Multiply the whole numbers 4 and 6.

That is,

4 x 6  =  24

The answer is reasonable. Because 24 is close to 23.4375.

Example 3 :

Chan Hee bought 3.4 pounds of cheese that cost $6.95 per pound. How much did he spend on cheese ?

Solution :

The cost of one pound of cheese  =  $6.95

To find the cost of 3.4 pounds of cheese, we have to multiply 3.4 and 6.95.

3.4 x 6.95  =  23.63

So, the cost of 3.4 pounds of cheese is $23.63.

Now, let us estimate to check whether our answer is reasonable.

Round 3.4 to the nearest whole number.

That is, 3

Round 6.95 to the nearest whole number.

That is, 7 

Multiply the whole numbers 3 and 7.

That is,

3 x 7  =  21

The answer is reasonable. Because 21 is close to 23.63.

Example 4 :

Adita earns $9.40 per hour working at an animal shelter. How much money will she earn for 18.5 hours of work ? 

Solution :

Earning in one hour  =  $9.40

To find the earning of 18.5 hours, we have to multiply 18.5 and 9.40

18.5 x 9.4  =  173.90

So, the earning for 18.5 hours is $173.90.

Now, let us estimate to check whether our answer is reasonable.

Round 18.5 to the nearest whole number.

That is, 19

Round 9.40 to the nearest whole number.

That is, 9 

Multiply the whole numbers 19 and 9.

That is,

19 x 9  =  171

The answer is reasonable. Because 171 is close to 173.90.

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