How do you solve problems with estimation?

Estimation is defined as guessing a value of a number close enough to the exact value to make it easier to calculate without making the resultant value inaccurate. Estimation and rounding off go hand in hand as both are interdependent on each other. There are some rules that an individual has to follow -

Rule 1:
You round up if the digit immediately to the right of the last significant figure is equal to or more than 5.

Rule 2:
You round down if the digit immediately to the right of the last significant figure is less than 5.

Let’s look at some examples to understand the following -

Example 1:

a. Estimate the value of 4.73 * 18.4
b. Use a calculator to find 4.73 * 18.4
c. Compare the estimate with the exact value

Solution :

a. 4.73 * 18.4 = 5 * 18 = 90
b. 4.73 * 18.4 = 87.032
c. Because in (a) we rounded both numbers, the estimate is slightly bigger than the actual value, but it does give us an idea of the size of the answer.

Example 2:

A cricket match is watched by 56,742 people. Write the number of people to the nearest.
a. 10,000
b. 1000
c. 10

Solution :

a. 56,742 = 60,000 to nearest 10,000.
b. 56742 = 57000 to nearest 1000
c. 56742 = 56740 to nearest 10

Example 3: John and Shawn love to collect marbles. John collected 233 and Shawn collected 842 marbles. What is the total number of marbles they have collected together? ( Round off your answer to the nearest tens).

Solution:

The number of marbles collected by John is 233.
Rounding to the nearest tens, 230 marbles.
The number of marbles collected by Shawn is 842.
Rounding to the nearest tens, 842 marbles.
Total number of marbles collected by both is 230 + 840 = 1070. So, 1070 is the better estimate.

Example 4: Sara uses her calculator to obtain her answer to,

Example 5:

Ana and sally decided to bake cupcakes for a family party. Ana baked 685 raisin cupcakes and sally baked 614 sugar cupcakes. How many cookies did they bake? Choose the better estimate. Round your answer to the nearest tens)

Solution :

The number of raisin cupcakes baked by Ana is 685.
Rounding to the nearest tense, 690 cookies.
The number of sugar cupcakes baked by Sally is 614.
Rounding to the nearest tens, 610 cupcakes.
The total number of cupcakes baked y both Ana and Sally is 690 + 610 = 1300 So, the better approximation is 1300 cupcakes.

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