ROUNDING TO NEAREST SIGNIFICANT FIGURES

Round off to the nearest 100 :

Problem 1 :

87

Solution :

i) 87 is between 0 and 100.

ii) 50 is the midpoint between 0 and 100.

iii) 87 is greater than the midpoint (50).

Therefore, 87 rounded to the nearest hundred = 100.

Problem 2 :

369

Solution :

i) 369 is between 300 and 400.

The digit in the 10's place is 6 > 5. So, we round it is 400.

Therefore, 369 rounded to the nearest hundred = 400.

Problem 3 :

442

Solution :

i) 442 is between 400 and 500.

ii) 450 is the midpoint between 400 and 500.

iii) 442 is less than the midpoint (450).

Therefore, 442 rounded to the nearest hundred = 400

Problem 4 :

650

Solution :

i) 650 is between 600 and 700.

ii) 650 is the midpoint between 600 and 700.

Therefore, 650 rounded to the nearest hundred = 700

Problem 5 :

991

Solution :

i) 991 is between 900 and 1000.

ii) 950 is the midpoint between 900 and 1000.

iii) 991 is greater than the midpoint (950).

Therefore, 991 rounded to the nearest hundred = 1000

Problem 6 :

1426

Solution :

i) 1426 is between 1400 and 1500.

ii) 1450 is the midpoint between 1400 and 1500.

iii) 1426 is less than the midpoint (1450).

Therefore, 1426 rounded to the nearest hundred = 1400

Problem 7 :

11,765

Solution :

i) 11,765 is between 11,700 and 11,800.

ii) 11,750 is the midpoint between 11,700 and 11,800.

iii) 11,765 is greater than the midpoint (11,750).

Therefore, 11,765 rounded to the nearest hundred = 11,800

Problem 8 :

34,037

Solution :

i) 34,037 is between 34,000 and 34,100.

ii) 34,050 is the midpoint between 34,000 and 34,100.

iii) 34,037 is less than the midpoint (34,050).

Therefore, 34,037 rounded to the nearest hundred = 34,000

Round off to the nearest 1000 :

Problem 1 :

784

Solution :

i) 784 is between 0 and 1000.

ii) 500 is the midpoint between 0 and 1000.

iii) 784 is greater than the midpoint (500).

Therefore, 784 rounded to the nearest thousand = 1000

Problem 2 :

5500

Solution :

i) 5500 is between 5000 and 6000.

ii) 5500 is the midpoint between 5000 and 6000.

Therefore, 5500 rounded to the nearest hundred = 6000

Problem 3 :

7435

Solution :

i) 7435 is between 7000 and 8000.

ii) 7500 is the midpoint between 7000 and 8000.

iii) 7435 is less than the midpoint (7500).

Therefore, 7435 rounded to the nearest thousand = 7000

Problem 4 :

9987

Solution :

i) 9987 is between 9000 and 10000.

ii) 9500 is the midpoint between 9000 and 10000.

iii) 9987 is greater than the midpoint (9500).

Therefore, 9987 rounded to the nearest thousand = 10000

Problem 5 :

12,324

Solution :

i) 12,324 is between 12,000 and 13,000.

ii) 12,500 is the midpoint between 12,000 and 13,000.

iii) 12,324 is less than the midpoint (12,500).

Therefore, 12,324 rounded to the nearest thousand = 12,000

Problem 6 :

23,497

Solution :

i) 23,497 is between 23,000 and 24,000.

ii) 23,500 is the midpoint between 23,000 and 24,000.

iii) 23,497 is less than the midpoint (23,500).

Therefore, 23,497 rounded to the nearest thousand = 23,000

Problem 7 :

53,469

Solution :

i) 53,469 is between 53,000 and 54,000.

ii) 53,500 is the midpoint between 53,000 and 54,000.

iii) 53,469 is less than the midpoint (53,500).

Therefore, 53,469 rounded to the nearest thousand = 53,000

Problem 8 :

670,934

Solution :

i) 670,934 is between 670,000 and 671,000.

ii) 670,500 is the midpoint between 670,000 and 671,000.

iii) 670,934 is greater than the midpoint (670,500).

Therefore, 670,934 rounded to the nearest thousand = 671,000

Round off to one significant figure :

Problem 1 :

69

Solution :

69 has 2 significant figures.

It is rounded to one significant figures is 70.

Problem 2 :

197

Solution :

197 has 3 significant figures.

It is rounded to one significant figures is 200.

Problem 3 :

293

Solution :

293 has 3 significant figures.

It is rounded to one significant figures is 300.

Problem 4 :

347

Solution :

347 has 3 significant figures.

It is rounded to one significant figures is 300.

Problem 5 :

963

Solution :

963 has 3 significant figures.

It is rounded to one significant figures is 1000.

Problem 6 :

2555

Solution :

2555 has 4 significant figures.

It is rounded to one significant figures is 3000.

Problem 7 :

6734

Solution :

6734 has 4 significant figures.

It is rounded to one significant figures is 7000.

Problem 8 :

39,500

Solution :

39,500 has 5 significant figures.

It is rounded to one significant figures is 40,000.

Round off to two significant figures :

Problem 1 :

891

Solution :

891 has 3 significant figures.

It is rounded to two significant figures is 890.

Problem 2 :

166

Solution :

166 has 3 significant figures.

It is rounded to two significant figures is 170.

Problem 3 :

750

Solution :

750 has 3 significant figures.

It is rounded to two significant figures is 750.

Problem 4 :

238

Solution :

238 has 3 significant figures.

It is rounded to two significant figures is 240.

Problem 5 :

561

Solution :

561 has 3 significant figures.

It is rounded to two significant figures is 560.

Problem 6 :

5647

Solution :

5647 has 4 significant figures.

It is rounded to two significant figures is 5600.

Problem 7 :

9750

Solution :

9750 has 4 significant figures.

It is rounded to two significant figures is 9800.

Problem 8 :

23501

Solution :

23501 has 5 significant figures.

It is rounded to two significant figures is 24000.

Round off to the accuracy given :

Problem 1 :

ϵ35,246 (to the nearest ϵ1000)

Solution :

i) 35,246 is between 35,000 and 36,000.

ii) 35,500 is the midpoint between 35,000 and 36,000.

iii) 35,246 is less than the midpoint (35,500).

Therefore, 35,246 rounded to the nearest thousand = 35,000

Problem 2 :

A distance of 3651 km (to the nearest 100 km)

Solution :

i) 3651 is between 3600 and 3700.

ii) 3650 is the midpoint between 3600 and 3700.

iii) 3651 is greater than the midpoint (3650).

Therefore, 3651 rounded to the nearest hundred = 3700

Problem 3 :

A donation of $375 (to one significant figure)

Solution :

$375 has 3 significant figures.

It is rounded to one significant figures is 400.

Problem 4 :

A house sold for £237,629 (to the nearest £10,000)

Solution :

A house sold for £237,629 rounded to the nearest ten thousand = 240,000

Problem 5 :

The attendance at a rock concert is 16723 (to the nearest thousand)

Solution :

i) 16,723 is between 16,000 and 17,000.

ii) 16,500 is the midpoint between 16,000 and 17,000.

iii) 16,723 is greater than the midpoint (16,500).

Therefore, 16,723 rounded to the nearest thousand = 17,000

Problem 6 :

The crowd is 35,381 people (to two significant figures)

Solution :

35,381 has 5 significant figures.

It is rounded to two significant figures is 35000.