# Estimation

Behavioural Objectives: At the end of the lesson, the pupils should be able to:

1. Write out the rules for estimation to nearest 10
2. Write out the estimate of each number given.

RULE 1: FOR 2 – DIGIT NUMBER

1. If the unit digit is less than 5, estimate to the lower nearest multiple of 10.
2. If the unit digit is greater than 5, estimate to the higher nearest multiple of 10.
3. If the unit digit is equal to 5, estimate to the higher nearest multiple of 5.

Example 1.
Write the estimate of the following numbers.
12, 14, 15, 17.
Solution
T u
1 2 > 10 since the expansion of 12 is 10+2 and 2 is the unit which is less than 5.

T u
1 4> 10= 10+4 and 4 is the unit digit which is less than 5.

T u
1 5> 20 since the expansion of 15 is 10+ 5 and 5 is the unit which is equal to 5.

T u
17> 20 since 7 which is 5 .

RULE 2: FOR 3 – DIGIT NUMBER

1. If the teens digit is less than 50, estimate to the lower nearest multiple of 100.
2. If the teens digit is greater than 50, estimate to the higher nearest multiple of 100.
3. If the teens digit is equal to 50, estimate to the higher nearest multiple of 100.

Example 1.
Write out the estimate multiples of 100.
121, 129, 236
Solution
H T U
1 2 1> 100 because 20<50.

H T U
1 2 9> 100 because 20<50.

H T U
2 3 6> 200 Because 30<50

RULE 3: FOR DECIMAL AND VULGAR NUMBER
Note: Vulgar numbers are simple numbers expressed with numerator and denominator. We estimate decimal and vulgar numbers to whole numbers.

RULE 3 FOR DECIMAL AND VULGAR NUMBERS.

1. If the decimal or fraction part is less than 0.5 or 1/2, estimate to nearest lower whole number.
2. If the decimal or fraction part is greater than 0.5 or 1/2, estimate to the nearest higher whole number.
3. If the decimal or fraction is equal to 0.5 or 1/2 estimate to the nearest higher whole number.

Example
Write out the estimate of the following decimal and fraction.

✳️3.2 = 3 because .2<5
3.5= 4 because .5=.5
✳️3¹/5= 3 because 1/5 <1/2 i.e 1/5 is 0.2 while 1/2 is 0.5

3½=4 because 1/2 = ½

ESTIMATION OF 2 DIGIT TO THE NEAREST 10.
Note: In estimation, a number is either rounded up or down to the nearest whole number.

1. Numbers less than 5 are rounded down.
2. Numbers greater than 5 are rounded up.

Example
Estimate the following 2 – digit number to their nearest 10.
54, 57, 22.
Solution
T u
5 4= 50 because 4 which is unit is not up to 5 .’. you rounded down.

(b). 57= 60 to the nearest tens

(c). 22= 20 because 2 is rounded down.

ESTIMATION OF 3 DIGIT WHOLE NUMBERS TO THE NEAREST 100 AND 4 DIGIT TO THE NEAREST 1000.

Example
Estimate the following 3 – digit to the nearest 100 and 4 digit to the nearest 1000.
(a)458 (b)704 (c) 6500 (d)4437
Solution
458= 500 to the nearest 100
704= 700 rounded down to the nearest 100
6500= 7000 rounded up to the nearest 1000
4437= 4000 rounded down to the nearest 1000.

Exercises.

1. Estimate the following 3 – digit to the nearest 109.
(a) 558 (b) 4648 (c) 7500
2. Estimate the following 2 digit to their nearest 10.
(a).55 (b). 69 (c). 74