MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES

Multiplying Significant Figures

Estimate using a one figure approximation :

Problem 1 :

389 × 63

Solution :

Rounding 389 :

In 389, 8 is greater than 5.

So, we are rounding it as 400.

Rounding 63 :

63, the unit digit is 3. Which is less than 5.

So, we are rounding it as 60.

= 400 × 60

= 24,000

Problem 2 :

4619 × 22

Solution :

Rounding 4619 :

In 4619, 6 is greater than 5.

So, we are rounding it as 5000.

Rounding 22 :

22, the unit digit is 2. Which is less than 5.

So, we are rounding it as 20.

= 5000 × 20

= 100,000

Problem 3 :

4062 × 638

Solution :

Rounding 4062 :

4062, the unit digit is 2. Which is less than 5.

So, we are rounding it as 4000.

Rounding 638 :

The numerical value that we find after 6 is 3, which is less than 5.

So, we are round 638 as 600.

= 4000 × 600

= 2,400,000

Problem 4 :

389 × 2178

Solution :

Rounding 389 :

In 389, 8 is greater than 5.

So, we are rounding it as 400.

Rounding 2178 :

The numerical value that we find after 2 is 1, which is less than 5.

So, we are round 2178 as 2000.

= 400 × 2000

= 800,000

Problem 5 :

588 × 11,642

Solution :

Rounding 588 :

In 588, 8 is greater than 5.

So, we are rounding it as 600.

Rounding 11642 :

In 11642, 1 is lesser than 5, so rounding it as 10000.

= 600 × 10000

= 6,000,000

Problem 6 :

29 × 675,328

Solution :

Rounding 29 :

29, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 30.

Rounding 675,328 :

675328 can be rounded as 700000.

= 30 × 700000

= 21,000,000

Dividing Significant Figures

Estimate the following using a one figure approximation :

Problem 1 :

641 ÷ 59

Solution :

Rounding 641 :

641 can be rounded as 600.

Rounding 59 :

59, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 60.

= 600 ÷ 60

= 10

Problem 2 :

2038 ÷ 49

Solution :

Rounding 2038 :

The numerical value that we find after 2 is 0, which is less than 5.

So, we are round 2038 as 2000.

Rounding 49 :

49, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 50.

= 2000 ÷ 50

= 40

Problem 3 :

5899 ÷ 30

Solution :

Rounding 5899 :

5899, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 6000.

Rounding 30 :

30, the unit digit is 3. Which is less than 5.

So, we are rounding it as 30.

= 6000 ÷ 30

= 200

Problem 4 :

2780 ÷ 41

Solution :

Rounding 2780 :

The numerical value that we find after 2 is 7, which is greater than 5.

So, we are round 2780 as 3000.

Rounding 41 :

41, the unit digit is 1. Which is less than 5.

So, we are rounding it as 40.

= 3000 ÷ 40

= 75

Problem 5 :

85,980 ÷ 299

Solution :

Rounding 85,980 :

From left to right after 8, we find 5. Then, we round 85,980 as 90,000.

Rounding 299 :

In 299, the digit after 2 is 9 and it is greater than 5.

So, we are rounding it as 300.

= 90,000 ÷ 300

= 300

Problem 6 :

36,890 ÷ 786

Solution :

Rounding 36,890 :

After 3, we have 6 and it is greater than 5.

So, we are round 36,890 as 40,000.

Rounding 786 :

786, the unit digit is 6. Which is greater than 5.

So, we are rounding it as 800.

= 40,000 ÷ 800

= 50

Estimate the Products of Multiplication

Estimate these products :

Problem 1 :

89 × 3

Solution :

Rounding 89 :

89, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 90.

3 is a single value.

= 90 × 3

= 270

Problem 2 :

57 × 9

Solution :

Rounding 57 :

57, the unit digit is 7. Which is greater than 5.

So, we are rounding it as 60.

9 is a single value.

= 60 × 9

= 540

Problem 3 :

62 × 6

Solution :

Rounding 62 :

62, the unit digit is 2. Which is less than 5.

So, we are rounding it as 60.

6 is a single value.

= 60 × 6

= 360

Problem 4 :

28 × 8

Solution :

Rounding 28 :

28, the unit digit is 8. Which is greater than 5.

So, we are rounding it as 30.

8 is a single value.

= 30 × 8

= 240

Problem 5 :

113 × 7

Solution :

Rounding 113 :

Rounding 113 as 100.

7 is a single value.

= 100 × 7

= 700

Problem 6 :

6895 × 6

Solution :

Rounding 6895 :

The numerical value after 6 is 8 and that is greater than 5.

So, we are rounding it as 7000.

6 is a single value.

= 7000 × 6

= 42,000

Problem 7 :

8132 × 8

Solution :

Rounding 8132 :

In 8132, the numerical value that we find after 8 is 1, which is less than 5.

So, we are rounding it as 8000.

8 is a single value.

= 8000 × 8

= 64,000

Problem 8 :

29,898 × 9

Solution :

Rounding 29,898 :

In 29898, the value that we find after 2 is 9, which is greater than 5.

So, we are rounding it as 30,000.

9 is a single value.

= 30,000 × 9

= 270,000

Estimating the Division

Use one figure approximations to estimate :

Problem 1 :

498 ÷ 5

Solution :

Rounding 498 :

Rounding 498 as 500.

5 is a single value.

= 500 ÷ 5

= 100

Problem 2 :

897 ÷ 3

Solution :

Rounding 897 :

In 897, the number that we find after 8 is 9, which is greater than 5. So, we are rounding it as 900.

3 is a single value.

= 900 ÷ 3

= 300

Problem 3 :

78,916 ÷ 4

Solution :

Rounding 78,916 :

The numerical value that we find after 7 is 8 and it is greater than 5. So, we are rounding it as 80,000.

4 is a single value.

= 80,000 ÷ 4

= 20,000

Problem 4 :

5908 ÷ 31

Solution :

Rounding 5908 :

In 5908, the numerical value that we find after 5 is 9 and it is greater than 5.So, we are rounding it as 6000.

Rounding 31 :

31, the unit digit is 1. Which is less than 5.

So, we are rounding it as 30.

= 6000 ÷ 30

= 200

Problem 5 :

697 ÷ 72

Solution :

Rounding 697 :

In 697, the number we find after 6 is 9 and it is greater than 5. So, we are rounding it as 700.

Rounding 72 :

72, the unit digit is 2. Which is less than 5.

So, we are rounding it as 70.

= 700 ÷ 70

= 10

Problem 6 :

8132 ÷ 41

Solution :

Rounding 8132 :

In 8132, the number that we find after 8 is 1 and it is less than 5.

So, we are rounding it as 8000.

Rounding 41 :

41, the unit digit is 1. Which is less than 5.

So, we are rounding it as 40.

= 8000 ÷ 40

= 200

Problem 7 :

3164 ÷ 98

Solution :

Rounding 3164 :

In 3164, the number that we find after 3 is 1 and it is less than 5. So, we are rounding it as 3000.

Rounding 98 :

98, the unit digit is 8. Which is greater than 5.

So, we are rounding it as 100.

= 3000 ÷ 100

= 30

Problem 8 :

6075 ÷ 29

Solution :

Rounding 6075 :

In 6075, the number that we find after 6 is 0 and it is less than 5. So, we are rounding it as 6000.

Rounding 29 :

29, the unit digit is 9. Which is greater than 5.

So, we are rounding it as 30.

= 6000 ÷ 30

= 200

Problem 9 :

6177 ÷ 104

Solution :

Rounding 6177 :

The numerical value that we find after 6 is 1, which is less than 5.

So, we are round 6177 as 6000.

Rounding 104 :

104, the unit digit is 4. Which is less than 5.

So, we are rounding it as 100.

= 6000 ÷ 100

= 60

Problem 10 :

9091 ÷ 58

Solution :

Rounding 9091 :

9091, the unit digit is 1. Which is less than 5.

So, we are rounding it as 9000

Rounding 58 :

58, the unit digit is 8. Which is greater than 5.

So, we are rounding it as 60.

= 9000 ÷ 60

= 150

Problem 11 :

4862 ÷ 195

Solution :

Rounding 4862 :

The numerical value that we find after 4 is 8, which is greater than 5.

So, we are rounding it as 5000.

Rounding 195 :

195, the unit digit is 5. Which is equal to 5.

So, we are rounding it as 200.

= 5000 ÷ 200

= 25

Problem 12 :

3956 ÷ 1970

Solution :

Rounding 3956 :

3956, the unit digit is 6. Which is greater than 5.

So, we are rounding it as 4000.

Rounding 1970 :

The numerical value that we find after 1 is 9, which is greater than 5.

So, we are rounding it as 2000.

= 5000 ÷ 200

= 2