Number System

Q1: Round each of the following numbers to the nearest ten:

i. 54

Last digit = 4 (less than 5)
So, round down to the nearest ten:
54 → 50
Answer: 50

ii. 327

Last digit = 7 (greater than or equal to 5)
So, round up to the nearest ten:
327 → 330
Answer: 330

iii. 2,793

Last digit = 3 (less than 5)
So, round down:
2,793 → 2,790
Answer: 2,790

iv. 8,049

Last digit = 9 (greater than or equal to 5)
So, round up:
8,049 → 8,050
Answer: 8,050

v. 12,345

Last digit = 5 (equal to 5)
So, round up:
12,345 → 12,350
Answer: 12,350

Q2: Round each of the following numbers to the nearest hundred:

i. 925

Tens digit = 2 (less than 5)
So, round down:
925 → 900
Answer: 900

ii. 6,854

Tens digit = 5 (equal to or greater than 5)
So, round up:
6,854 → 6,900
Answer: 6,900

iii. 41,263

Tens digit = 6 (greater than 5)
So, round up:
41,263 → 41,300
Answer: 41,300

iv. 27,861

Tens digit = 6 (greater than 5)
So, round up:
27,861 → 27,900
Answer: 27,900

v. 5,549

Tens digit = 4 (less than 5)
So, round down:
5,549 → 5,500
Answer: 5,500

Q3: Round each of the following numbers to the nearest thousand:

i. 7,386

Rounding to nearest 1,000 → Look at hundreds place (3)
Since 3 < 5 → Round down
7,000

ii. 34,276

Hundreds digit is 2 → Round down
34,000

iii. 23,804

Hundreds digit is 8 → Round up
24,000

iv. 76,540

Hundreds digit is 5 → Round up
77,000

Q4: Find the approximate sum to the nearest ten:

i. (72 + 37)

Round off: 72 → 70, 37 → 40
70 + 40 = 110

ii. (264 + 348)

264 → 260, 348 → 350
260 + 350 = 610

iii. (2,538 + 6,274)

2,538 → 2,540, 6,274 → 6,270
2,540 + 6,270 = 8,810

iv. (4,782 + 2,345)

4,782 → 4,780, 2,345 → 2,350
4,780 + 2,350 = 7,130

Q5: Find the approximate sum to the nearest hundred:

i. (347 + 476)

347 → 300, 476 → 500
300 + 500 = 800

ii. (654 + 247)

654 → 700, 247 → 200
700 + 200 = 900

iii. (5,240 + 3,421)

5,240 → 5,200, 3,421 → 3,400
5,200 + 3,400 = 8,600

iv. (9,483 + 6,572)

9,483 → 9,500, 6,572 → 6,600
9,500 + 6,600 = 16,100

Q6: Find the approximate sum to the nearest thousand:

i. (43,728 + 36,275)

43,728 → 44,000, 36,275 → 36,000
44,000 + 36,000 = 80,000

ii. (37,804 + 22,475)

37,804 → 38,000, 22,475 → 22,000
38,000 + 22,000 = 60,000

iii. (6,785 + 2,476)

6,785 → 7,000, 2,476 → 2,000
7,000 + 2,000 = 9,000

Q7: Find the approximate difference to the nearest ten:

i. (64 – 29)

Rounded: 64 → 60, 29 → 30
60 – 30 = 30

ii. (186 – 49)

Rounded: 186 → 190, 49 → 50
190 – 50 = 140

iii. (429 – 206)

Rounded: 429 → 430, 206 → 210
430 – 210 = 220

Q8: Find the approximate difference to the nearest hundred:

i. (769 – 435)

Rounded: 769 → 800, 435 → 400
800 – 400 = 400

ii. (859 – 675)

Rounded: 859 → 900, 675 → 700
900 – 700 = 200

iii. (8,359 – 4,317)

Rounded: 8,359 → 8,400, 4,317 → 4,300
8,400 – 4,300 = 4,100

Q9: Find the approximate difference to the nearest thousand:

i. (45,783 – 38,695)

Rounded: 45,783 → 46,000, 38,695 → 39,000
46,000 – 39,000 = 7,000

ii. (38,005 – 29,375)

Rounded: 38,005 → 38,000, 29,375 → 29,000
38,000 – 29,000 = 9,000

iii. (7,654 – 4,368)

Rounded: 7,654 → 8,000, 4,368 → 4,000
8,000 – 4,000 = 4,000

Q10: Estimate each of the following products by rounding off each number to the nearest ten:

i. (49 × 72)

Rounded: 49 → 50, 72 → 70
50 × 70 = 3,500

ii. (39 × 62)

Rounded: 39 → 40, 62 → 60
40 × 60 = 2,400

iii. (63 × 57)

Rounded: 63 → 60, 57 → 60
60 × 60 = 3,600

iv. (35 × 43)

Rounded: 35 → 40, 43 → 40
40 × 40 = 1,600

Q11: Estimate each of the following products by rounding off each number to the nearest hundred:

i. (264 × 334)

Rounded: 264 → 300, 334 → 300
300 × 300 = 90,000

ii. (457 × 872)

Rounded: 457 → 500, 872 → 900
500 × 900 = 4,50,000

iii. (381 × 316)

Rounded: 381 → 400, 316 → 300
400 × 300 = 1,20,000

iv. (455 × 138)

Rounded: 455 → 500, 138 → 100
500 × 100 = 50,000

Q12: Find the approximate quotient for each of the following:

i. (86 ÷ 27)

Rounded: 86 → 90, 27 → 30
90 ÷ 30 = 3

ii. (83 ÷ 19)

Rounded: 83 → 80, 19 → 20
80 ÷ 20 = 4

iii. (286 ÷ 25)

Rounded: 286 → 300, 25 → 30
300 ÷ 30 = 10

iv. (865 ÷ 38)

Rounded: 865 → 900, 38 → 40
900 ÷ 40 = 22.5 → 23