Part I Exercise 1.4
Understanding Based Questions
1. Estimate the numbers as instructed:
a. 5428 (Estimate to nearest 10s)
Ans: The digit at the ones place is 8 (8 > 5). Therefore, the tens digit is rounded up by 1, and the ones digit becomes 0. → 5,430
b. 9999999 (Estimate to nearest 100s)
Ans: The digit at the tens place is 9 (9 > 5). Rounding up adds a carry-over across all places. → 1,00,00,000
c. 307184 (Estimate to nearest 1000s)
Ans: The digit at the hundreds place is 1 (1 < 5). Therefore, the thousands digit remains unchanged, and subsequent digits become 0. → 3,07,000
d. 9003727 (Estimate to nearest 100s)
Ans: The digit at the tens place is 2 (2 < 5). Therefore, the hundreds digit remains unchanged, and subsequent digits become 0. → 90,03,700
e. 6304 ÷ 942
Ans: Rounding off to the nearest thousands and hundreds respectively for general estimation:
6,304 → 6,000
942 → 900
Estimated Value: 6,000 ÷ 900 = 60 ÷ 9 = 6.67
f. 9731 + 4675
Ans: Rounding off both numbers to the nearest thousands:
9,731 → 10,000
4,675 → 5,000
Estimated Sum: 10,000 + 5,000 = 15,000
g. 7734 – 5415
Ans: Rounding off both numbers to the nearest thousands:
7,734 → 8,000
5,415 → 5,000
Estimated Difference: 8,000 – 5,000 = 3,000
h. 18035 ÷ 1834
Ans: Rounding off to compatible leading values:
18,035 → 18,000
1,834 → 2,000
Estimated Quotient: 18,000 ÷ 2,000 = 9
Application Based Questions
2. Solve it to the nearest tens:
a. 37 + 91
Sol: 37 → 40 | 91 → 90
Estimated Value = 40 + 90 = 130
b. 810 + 144
Sol: 810 → 810 | 144 → 140
Estimated Value = 810 + 140 = 950
c. 67 – 24
Sol: 67 → 70 | 24 → 20
Estimated Value = 70 – 20 = 50
d. 165 ÷ 11
Sol: 165 → 170 | 11 → 10
Estimated Value = 170 ÷ 10 = 17
e. 261 – 184
Sol: 261 → 260 | 184 → 180
Estimated Value = 260 – 180 = 80
f. 368 × 115
Sol: 368 → 370 | 115 → 120
Estimated Value = 370 × 120 = 44,400
g. 424 ÷ 71
Sol: 424 → 420 | 71 → 70
Estimated Value = 420 ÷ 70 = 6
h. 481 + 324
Sol: 481 → 480 | 324 → 320
Estimated Value = 480 + 320 = 800
3. Solve to the nearest hundreds:
a. 324 + 101
Sol: 324 → 300 | 101 → 100
Estimated Value = 300 + 100 = 400
b. 647 – 371
Sol: 647 → 600 | 371 → 400
Estimated Value = 600 – 400 = 200
c. 118 × 384
Sol: 118 → 100 | 384 → 400
Estimated Value = 100 × 400 = 40,000
d. 6674 × 1487
Sol: 6,674 → 6,700 | 1,487 → 1,500
Estimated Value = 6,700 × 1,500 = 1,00,50,000
4. Solve to the nearest thousands:
a. 8147 + 6482
Sol: 8,147 → 8,000 | 6,482 → 6,000
Estimated Value = 8,000 + 6,000 = 14,000
b. 2481 + 9764
Sol: 2,481 → 2,000 | 9,764 → 10,000
Estimated Value = 2,000 + 10,000 = 12,000
c. 9901 – 1847
Sol: 9,901 → 10,000 | 1,847 → 2,000
Estimated Value = 10,000 – 2,000 = 8,000
d. 6405 × 3142
Sol: 6,405 → 6,000 | 3,142 → 3,000
Estimated Value = 6,000 × 3,000 = 1,80,00,000
e. 21348 ÷ 3481
Sol: 21,348 → 21,000 | 3,481 → 3,000
Estimated Value = 21,000 ÷ 3,000 = 7
f. 7944 × 8142
Sol: 7,944 → 8,000 | 8,142 → 8,000
Estimated Value = 8,000 × 8,000 = 6,40,00,000
g. 83015 – 41164
Sol: 83,015 → 83,000 | 41,164 → 41,000
Estimated Value = 83,000 – 41,000 = 42,000
h. 39916 ÷ 7587
Sol: 39,916 → 40,000 | 7,587 → 8,000
Estimated Value = 40,000 ÷ 8,000 = 5
5. Find the estimated value of 844 × 621.
Sol: Rounding off both numbers to the nearest hundreds:
• 844 is rounded off to 800 (Since tens digit 4 < 5)
• 621 is rounded off to 600 (Since tens digit 2 < 5)
Estimated Product: 800 × 600 = 4,80,000
6. Find the estimated value of 34197 + 9476 – 21647.
Sol: Rounding off numbers to the nearest thousands:
• 34,197 is rounded off to 34,000
• 9,476 is rounded off to 9,000
• 21,647 is rounded off to 22,000 (Since hundreds digit 6 > 5)
Estimated Value: 34,000 + 9,000 – 22,000
= 43,000 – 22,000 = 21,000
7. Find the estimated quotient of 6550 ÷ 2184.
Sol: Rounding off both numbers to the nearest thousands:
• 6,550 is rounded off to 7,000 (Since hundreds digit is 5 = 5)
• 2,184 is rounded off to 2,000
When we divide 7000/2000 we will get the quitent as 3 and reminder 1000.
8. Find the estimated expenses of Vinod, if he bought a television for ₹54,673, a washing machine for ₹18,347 and refrigerator for ₹34,847.
Sol: To find the estimated expenses, we will round off each amount to the nearest thousands.
- Cost of Television = ₹54,673 (rounds off to ₹55,000)
- Cost of Washing Machine = ₹18,347 (rounds off to ₹18,000)
- Cost of Refrigerator = ₹34,847 (rounds off to ₹35,000)
Calculation:
Estimated Total Expenses = ₹55,000 + ₹18,000 + ₹35,000
Estimated Total Expenses = ₹1,08,000
Answer: The estimated expenses of Vinod are ₹1,08,000.