## 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**