MULTIPLYING AND DIVIDING SIGNIFICANT FIGURES WORD PROBLEMS

Estimate the cost of :

Problem 1 :

59 pens at $4 each

Solution :

Number of pens = 59

Rounding 59 :

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

So, we are rounding it as 60.

Cost of each pen = $4

= 60 × 4

= $240

Problem 2 :

77 books at $8 each

Solution :

Number of books = 77

Cost of each book = $8

Rounding 77 :

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

So, we are rounding it as 80.

= 80 × 8

= $640

Problem 3 :

208 staplers at 87 each

Solution :

Number of staplers = 208

Cost of each stapler = $7 

Rounding 208 :

The numerical value that we find before 8 is 0, which is less than 5.

So, we are rounding 208 as 200.

= 200 × 7

= $1400

Problem 4 :

4079 rolls of tape at $9 each

Solution :

Number of rolls of tape = 4079

Cost of each rolls of tape = $9

Rounding 4079 :

The numerical value that we find before 4 is 0, which is less than 5.

So, we are rounding 4079 as 4000.

= 4000 × 9

= $36,000

Estimate the cost of :

Problem 5 :

48 books at $19 each

Solution :

Number of books = 48

Cost of each books = $19

Rounding 48 :

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

So, we are rounding it as 50.

Rounding 19 :

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

So, we are rounding it as 20.

= 50 × 20

= $1000

Problem 6 :

82 calculators at ϵ28 each

Solution :

Number of calculators = 82

Cost of each calculator = ϵ28

Rounding 82 :

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

So, we are rounding it as 80.

Rounding 28 :

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

So, we are rounding it as 30.

= 80 × 30

= ϵ2400

Problem 7 :

69 concert tickets at £48 each

Solution :

Number of concert tickets = 69

Cost of each concert ticket = £48

Rounding 69 :

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

So, we are rounding it as 70.

Rounding 48 :

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

So, we are rounding it as 50.

= 70 × 50

= £3500

Problem 8 :

89 CD players at $59 each

Solution :

Number of CD players = 89

Cost of each CD player = $59

Rounding 89 :

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

So, we are rounding it as 90.

Rounding 59 :

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

So, we are rounding it as 60.

= 90 × 60

= $5400

Problem 9 :

a. Estimate how much each person would get if a ϵ489,555 lottery prize is equally divided amongst 18 friends.

b. Estimate how long it would take Andreas to type a 7328 word article for a magazine if he type at 68 words per minute.

Solution :

a. Lottery prize = ϵ489,555

Number of friends = 18

Rounding 489,555 :

489555, the unit digit is 5. Which is equal to 5.

So, we are rounding it as 500,000.

Rounding 18 :

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

So, we are rounding it as 20.

= 500,000 ÷ 20

= ϵ25,000

b. Number of words = 7328

He type at 68 words per minute.

Rounding 7328 :

7328, the unit digit is 8. Which is greater than 5.

So, we are rounding it as 7000.

Rounding 68 :

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

So, we are rounding it as 70.

= 7000 ÷ 70

= 100

In each of the following, use one figure approximation to estimate the answer.

Problem 10 :

Helga can type at a rate of 58 words per minute. Estimate the number of words she can type in 38 minutes.

Solution :

Number of words = 58

The number of words she can type in 38 minutes.

Rounding 58 :

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

So, we are rounding it as 60.

Rounding 38 :

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

So, we are rounding it as 40.

= 60 × 40

= 2400 words

So, she can type 2400 words in 38 minutes.

Problem 11 :

An apple orchard contains 72 rows of apple trees with 38 trees per row.

i. Estimate the number of apple trees in the orchard.

ii. Suppose each tree has yields on average of 278 apples. Estimate the total number of apples picked from the orchard.

Row of apple trees = 72

Number of trees = 38

Rounding 72 :

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

So, we are rounding it as 70.

Rounding 38 :

38, the unit digit is 8, which is greater than 5.

So, we are rounding it as 40.

= 70 × 40

= 2800 trees

So, the number of apple trees in the orchard is 2800 trees.

ii. Average number of apple = 278 

Rounding 278 :

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

So, we are rounding it as 300.

= 300 × 2800

= 840,000 apples

So, the total number of apples picked from the orchard is 840,000.

Problem 12 :

A wine vat holds 29,675 litres of wine. The wine is siphoned into barrels for ageing, if each barrel holds 1068 litres of wine, how many barrels are needed ?

Solution :

Quantity of wine = 29,675

Quantity of wine in each barrels = 1068

Rounding 29,675 :

29,675, the unit digit is 5. Which is equal to 5.

So, we are rounding it as 30,000.

Rounding 1068 :

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

So, we are round 1068 as 1000.

= 30,000 ÷ 1000

= 30 barrels

Hence, 30 barrels are needed.

Problem 13 :

Michael wants to tow his boat on a trailer between two cities which are 468 km apart. It is a big boat so his car can only average 52 km per hour while towing. How long will the journey take Michael ?

Solution :

Distance between two cities = 468 km

Average 52 km per hour while towing.

Rounding 468 :

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

So, we are rounding it as 500.

Rounding 52 :

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

So, we are rounding it as 50.

= 500 ÷ 50

= 10 hours

So, length will the journey take Michael is 10 hours.

Problem 14 :

A concert hall has 87 rows of seats, each with 58 seats. The cost per seat is $32.

i. Estimate the total number of seats

ii. Estimate the total income if all seats are sold.

Solution :

Number of seats in row = 87

Each with 58 seats.

Cost of a seat = $32

i. Rounding 87 :

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

So, we are rounding it as 90.

Rounding 58 :

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

So, we are rounding it as 60.

= 90 × 60

= 5400 seats

Hence, total number of seats = 5400.

ii. Total number of seats = 5400

Cost per seat = $32

Rounding 32 :

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

So, we are rounding it as 30.

= 5400 × 32

= $162,000