Estimation and Approximation

Q1: Population of a city was 3,54,976 in the year 2014. In the year 2015, it increased by 68,438. What was the population of the city at the end of the year 2015?

Step 1: Population in 2014 = 3,54,976

Step 2: Increase in 2015 = 68,438

Step 3: Total population at end of 2015 = 3,54,976 + 68,438
3,54,976 + 68,438 = 4,23,414

Final Answer: 4,23,414

Q2: A = 7,43,000 and B = 8,00,100. Which is greater A or B? And by how much?

Q3: A notebook has 56 pages. How many pages will 5326 such notebooks have?

Q4: A person has 75,000 sheets of paper. If each sheet makes 8 pages of a notebook, how many notebooks of 200 pages can be made using the above sheets?

Q5: Add 1,7,209 ; 4,50,923 and 44,83,947.

Q6: A cricket player has scored 7,849 runs so far in test matches. He wishes to complete 10,000 runs; how many more runs does he need?

Q7: In an election two candidates A and B are the only contestants. If candidate A scored 9,32,567 votes and candidate B scored 9,00,235 votes, by how much margin did A win or loose the election?

Q8: Find the difference between the largest and the smallest five digit numbers that can be formed using the digits 5, 1, 6, 3 and 2 without repeating any digit.

Q9: A machine manufactures 5,782 screws every day. If we round off the number of screws produced in a day to the nearest thousand, approximately how many screws will the machine manufacture in the month of April?

Q10: A man has 1,57,184 with him. He placed an order for purchasing 80 articles at 125 each. How much money will remain with him after the purchase?

Q11: A student multiplied 8,035 by 87 instead of multiplying by 78. By how much was his answer greater than or less than the correct answer?

Incorrect Calculation:
8035 × 87 = 699,045

Correct Calculation:
8035 × 78 = 626,730

Difference in Answers:
699045 − 626730 = 72,315

Conclusion:
The student’s answer was 72,315 greater than the correct answer.

Q12: Mohani has 30 m cloth and she wants to make some shirts for her son. If each shirt requires 2 m 30 cm cloth, how many shirts, in all, can be made and how much length of the cloth will be left?

Convert 2 m 30 cm to meters:
2 m 30 cm = 2 + 0.30 = 2.30 m

Divide total cloth by cloth per shirt:
30 ÷ 2.30 = 13.04

So, number of full shirts:
= 13 shirts

Cloth used for 13 shirts:
13 × 2.30 = 29.90 m

Cloth left:
30 − 29.90 = 0.10 m or 10 cm

Q13: The weight of a box is 4 kg 859 g. What will be the approximate weight of 150 such boxes if we round off the weight of each box to 5 kg?

Rounded weight per box:
≈ 5 kg

Weight of 150 boxes:
5 × 150 = 750 kg

Q14: The distance between two places A and B is 3 km 760 m. A boy travels from A to B and then B to A every day. How much distance does he travel in 8 days?

Total distance per day (A to B and back):
= 2 × 3.760 km = 7.520 km

Distance in 8 days:
7.520 × 8 = 60.16 km

Q15: An oil-tin contains 6 litre and 60 ml oil. How many identical bottles can this oil fill, if the capacity of each bottle is 30 ml?

Convert 6 litre 60 ml to ml:
6 litre = 6000 ml
Total = 6000 + 60 = 6060 ml

Number of bottles:
6060 ÷ 30 = 202 bottles

Q16: The sale receipt of a company in a certain year was ₹ 83,73,540. In the following year, it decreased by ₹ 7,84,670.

i. What was the sale receipt of the company during the following year?
Sale receipt in the following year:
8373540 − 784670 = ₹75,88,870

ii. What was the total sale receipt of the company during these two years?
Total receipt for two years:
8373540 + 7588870 = ₹1,59,62,410

Q17: A number exceeds 8,59,470 by 3,00,999. What is the number?

859470 + 300999 = 11,60,469

Q18: Estimate the product of 5273 and 1208 by rounding off each number to the nearest hundred. Now calculate the actual product of the two numbers and find the difference between the actual product and the estimate.

Estimate:
5273 ≈ 5300, 1208 ≈ 1200
Estimated product = 5300 × 1200 = 63,60,000

Actual product:
5273 × 1208 = 63,69,784

Difference:
6368984 − 6360000 = 9,784