Approximation

Rounding off Numbers to the Nearest 10, 100 and 1000

You recall that powers of ten as 10¹, 10², 10³ are 10, 100,  1000 etc. respectively. When rounding off to any of these powers of ten, numbers half or above half of 10 are rounded off by adding one to the required digit, while the remaining lower digits are dropped to zero.

Example 1

Round off 253 718 to the nearest thousand.

Solution

The thousand digits is 3, and the digit before it is 7.

Since 7 is higher than 5, hence it is rounded up to 10 and 1 is added to 3 to become 4, and the remaining digits are replaced with zero. That is;

253 718 = 254 000 to the nearest 1 000. This is because 718 is nearer to 1 000 than to 418 or 7 is nearer to 10 than it is to zero. This is known as rounding up.

Example 2

Round off 25 467 to nearest ten, and state the type of rounding off.

Solution

The ten digit is 6, and the digit before it is 7. As 7 is higher than 5, 1 is added to 6 to become 7.

∴ 25 467 = 25 470 this type is rounding up.

Example 3

Round off 46 960 to the nearest hundred.

Solution

The hundred digit is 9, and the digit before it is 6. As 6 is higher than 5, 1 is added to 9 to become 10, hence 1 is added to 6 to become 7 and the remaining digits are replaced with zero.

∴ 46 960 = 47 000 (nearest hundred)

Class Activity

1. Approximate the following to the nearest: a) ten b) hundred c) thousand

(i) 67 548  (ii) 548997  (iii) 81 062  (iv) 90 638  (v) 178 654

2. In 2008, the value of a plot of land was #238 000. Its value rises by about 10% each year. Estimate its value in 2009 to the nearest #1000.

Application of Approximation in Everyday Life

Approximation is done in everyday activities. For example, two students can approximate the distances between their respective homes and the school to know who comes from a distant place. Also, the price of various commodities can also be approximated.

Areas in which approximation are applicable

(i) Purchase of household commodity

(ii) Measurement of distance from one place to another

(iii) Government use approximation as a tool in preparing budget

(iv) Scientists make use of approximation in many of their calculations

(v) Many financial institutions make use approximation in their day to day transaction

Example

1. A sum of #236 000 is divided equally among 54 members of a club. Approximate how much each student will get to the nearest: i) tenth ii) hundred iii) thousand

Solution

#236 000 ÷ 54 = #4 370.37

(i) #4 370.4 to the nearest tenth

(ii) #4 400.00 to the nearest hundred

(iii) #4 000.00 to the nearest thousand

2. Amina is in her school library committee that is planning to provide additional shelves for the 580 new books recently donated. Each shelf can hold about 28 books. About how many additional shelves would be needed?

Solution

580 is about 600.

28 is about 30

So, 580 ÷ 28 is about 600 ÷ 30

= 20 shelves.

Quantitative Reasoning

Sample

1. 8  *  4   =   8  +   4  =  12

(16  *  8). 4  =  16  +  8 ÷ 4

= 24  ÷ 4

= 6

2. 8 _ 4  =  8 ÷ 4 = 2

(16­_8) * 4 = (16 ÷ 8) + 4

= 2  + 4

= 6

CLASS ACTIVITY

1. Solve the following: (i) (25 * 10).5  (ii) (60 _ 12) * 6

PRACTICE QUESTIONS

1. The total mass of 8 mangoes is 965g. Fatima bought 5kg mangoes. Calculate the number of mangoes she bought approximately to the nearest i) tenth ii) whole number.
2. Solve the following: (i) (48_6)(6∗2) (ii) (1_4)(1∗3)
3. The perimeter of a school compound is 1 616m. in the perimeter of the fence, there are 203 fence posts equally spaced. Find the approximate distance between any posts?
4. Round off the following to the nearest (a) thousand  (b) hundred  (c) tens

(i) 18 654  (ii) 26 888  (iii) 12 505  (iv) 45 072  (v) 9 895

5. A man’s hand-span is 22cm. He finds that the height of a door is about nine hands-spans. Find the approximate height of the door.

ASSIGNMENT

1. A farmer has #200 000 to spend on cattle. He wants to buy 9 calves. Each calf costs #18 500. Check, by approximation, that the farmer has enough money. Find, accurately, how much change he will get after buying the calves.
2. A teacher gave a group of 45 students a test in mathematics. The average score was 21.5 marks. Estimate the total score in the test for the student.
3. A motorist travelled with a speed limit of 214km/h from one town to another. What was the total distance covered in 2hours to the nearest kilometres?
4. The number of bags of rice in a store is 125 and the number of beans in the same store is 68. Find the total number of bags of rice and beans in the store to the nearest:

(a) ten  (b) hundred  (c) 1 significant figure  (d) whole number

5. A jug contains 2½ litres of water. Find the approximate number of jugs of water in a drum containing 150¹/₃ litres of water.