NCERT Solution Exercise 1.3
Question (1) Estimate each of the following using general rule:
(a) 730 + 998
Solution
Given, 730 + 998
After the estimation 730 will be 700 and 998 will be 1000
= 700 + 1000
= 1700
Thus, after the estimation the sum of given numbers = 1700 Answer
(b) 796 – 314
Solution
Given, 796 – 314
After estimation 796 will become 800
And, 314 will become 300
Thus, after estimation
796 – 314 = 800 + 300
= 500
Thus, after estimation
796 – 314 = 800 + 300 = 500 Answer
(c) 12,904 + 2,888
Solution
Given, 12,904 + 2,888
After estimation 12,904 will become 13,000
And, 2,888 will become 3,000
Thus, 12,904 + 2,888
= 1,3000 + 3,000 = 16,000
Thus, After the estimation the sum of given numbers = 16,000 Answer
(d) 28,292 – 21,496
Solution
Given, 28,292 – 21,496
After estimation 28,292 will become 28,000
And, 21,496 will become 21000
Thus, 28,292 – 21,496
= 28,000 – 21000
= 7000
Thus, Answer = 7000
Question (2) Given a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens):
(a) 439 + 334 + 4,317
Solution
Given, 439 + 334 + 4,317
Estimation by rounding off to nearest hundreds
439 will become 400
334 will be equal to 300
And, 4.317 will become 4,300
Thus, 439 + 334 + 4,317
= 400 + 300 + 4,300
= 5,000
Thus, after rounding off the given number to nearest hundred the sum = 5,000
Estimation by rounding off to nearest tens
439 will become 440
334 will be equal to 330
And, 4.317 will become 4,320
Thus, 439 + 334 + 4,317
= 440 + 330 + 4,320
= 5,090
Thus, after rounding off the given number to nearest hundred the sum = 5,090
Thus, sum of the given numbers after rounding off to the nearest hundreds and after rounding off to the nearest tens = 5,000 and 5,090 Answer
(b) 1,08,734 – 47,599
Solution
Given, 1,08,734 – 47,599
Estimation by rounding off to nearest hundreds
1,08,734 will become 1,08,700
And, 47,599 will be equal to 47,600
Thus, 1,08,734 – 47,599
= 1,08,700 – 47,600
= 61,100
Thus, after rounding off the given number to nearest hundred the sum = 61,100
Estimation by rounding off to nearest tens
Given, 1,08,734 – 47,599
1,08,734 will become 1,08,730
And, 47,599 will be equal to 47,600
Thus, 1,08,734 – 47,599
= 1,08,730 – 47,600
= 61,130
Thus, after rounding off the given number to nearest hundred the sum = 61,130
Thus, difference of the given numbers after rounding off to the nearest hundreds and after rounding off to the nearest tens = 61,100 and 61,130 Answer
(c) 8,325 – 491
Solution
Given, 8,325 – 491
Estimation by rounding off to nearest hundreds
8,325 will become 8,300
And, 491 will be equal to 500
Thus, 8,325 – 491
= 8300 – 500
= 7,800
Thus, after rounding off the given number to nearest hundred the sum = 7800
Estimation by rounding off to nearest tens
Given, 8,325 – 491
8,325 will become 8,330
And, 491 will be equal to 490
Thus, 8,325 – 491
= 8,330 – 490
= 7,840
Thus, after rounding off the given number to nearest hundred the sum = 4,840
Thus, difference of the given numbers after rounding off to the nearest hundreds and after rounding off to the nearest tens = 7,800 and 7,840 Answer
(d) 4,89,348 – 48,365
Solution
Given, 4,89,348 – 48,365
Estimation by rounding off to nearest hundreds
4,89,348 will become 4,89,300
And, 48,365 will be equal to 48,400
Thus, 4,89,348 – 48,365
= 4,89,300 – 48,400
= 4,40,900
Thus, after rounding off the given number to nearest hundred the sum = 4,40,900
Estimation by rounding off to nearest tens
Given, 4,89,348 – 48,365
4,89,348 will become 4,89,350
And, 48,365 will be equal to 48,370
Thus, 4,89,348 – 48,365
= 4,89,350 – 48,370
= 4,40,980
Thus, after rounding off the given number to nearest hundred the sum = 4,40,980
Thus, difference of the given numbers after rounding off to the nearest hundreds and after rounding off to the nearest tens = 4,40,900 and 4,40,980 Answer
Question (3) Estimate the following products using general rule:
(a) 578 × 161
Solution
Given, 578 × 161
Estimation by rounding off using general rule
578 will become 600
And, 161 will be equal to 200
Thus, 578 × 161
= 600 × 200
= 1,20,000
Thus, the product of the given numbers after rounding off using general rule = 1,20,000 Answer
(b) 5281 × 3491
Solution
Given, 5281 × 3491
Estimation by rounding off using general rule
5281 will become 5000
And, 3491 will be equal to 3500
Thus, 5281 × 3500
= 5000 × 3500
= 1,75,00,000
Thus, the product of the given numbers after rounding off using general rule = 1,75,00,000 Answer
(c) 1291 × 592
Solution
Given, 1291 × 592
Estimation by rounding off using general rule
1291 will become 1300
And, 592 will be equal to 600
Thus, 1291 × 592
= 1300 × 600
= 7,80,000
Thus, the product of the given numbers after rounding off using general rule = 7,80,000 Answer
(d) 9250 × 29
Solution
Given, 9250 × 29
Estimation by rounding off using general rule
9250 will become 10,000
And, 29 will be equal to 30
Thus, 9250 × 29
= 10000 × 30
= 3,00,000
Thus, the product of the given numbers after rounding off using general rule = 3,00,000 Answer