When estimating we usually round each number to one significant figure and evaluate the result. We call this a one figure approximation.
When estimating we usually round each number to one significant figure and evaluate the result. We call this a one figure approximation.
In the following questions, round the given data to one significant figure to estimate the value asked for.
Problem 1 :
Tracy delivers 405 papers on a paper round. She does this every week for a year. Estimate the number of papers delivered in the year.
Solution :
Number of papers on a paper round = 405
Number of weeks in a year = 52
Total number of papers delivered in a year = 405 x 52
Rounding each number to the significant figure,
= 400 x 50
= 20000 papers
Problem 2 :
In the school dining hall there are 18 benches, each with 12 chairs. Estimate the number of chairs in the dining hall.
Solution :
Number of benches in the hall = 18
Number of chairs in each bench = 12
Total number of chairs = 18 x 12
Rounding to the significant figure, we get
= 20 x 10
= 200 chairs.
So, approximated number of chairs is 200.
Problem 3 :
In 2006, an average of 1071 flights were scheduled to arrive in or depart from Dubai each day. If they each carried an average of 84 people, estimate the number of passengers handled by Dubai International Airport each day.
Solution :
Number of flight arrived = 1071
Number of people in each flight = 84
Total number of passengers = 1071 x 84
Rounding to one significant figure,
= 1000 x 80
= 80000
So, number of passengers handled by Dubai International Airport on each day is 80000.
Problem 4 :
Tim counted 42 jelly beans in the bottom layer of a jar. He thinks that there are 38 layers in the jar. Estimate the number of jelly beans in the jar.
Solution :
Number of Jelly beans in a bottom layer = 42
Number of layers in the jar = 38
Number of jelly beans = 42 x 38
Rounding to one significant figure,
= 40 x 40
= 1600 Jelly beans
So, the number of jelly beans is 1600.
Problem 5 :
Sally earned $404 per week for 7 months of the year. Estimate the total amount of money she earned.
Solution :
Amount she earned per week = 404
Number of weeks per month = 4
Number of months she is earning = 7 months
Number of weeks for all 7 months = 7 x 4
= 28 weeks
Amount of money she has earned = 404 x 28
Rounding to one significant figure,
= 400 x 30
= $12000
So, her total earning is $12000.
Problem 6 :
It took me 11 hours to drive the 1057 km from Calgary to Vancouver. Estimate my average speed in kilometres per hour.
Solution :
Distance to be covered form Calgary to Vancouver = 1057
Time taken = 11 hours
Average speed = Total distance covered / total time taken
= ( 1057 )/11
Rounding to one significant figure, we get
= 1000/10
= 100
So, average speed is 100 km per hour.
Problem 7 :
A mathematics teacher gives one test a week to his class of 31 students. Estimate the number of tests the teacher will mark in 39 weeks.
Solution :
Total number of students in the class = 31
Number of test she gives in a week = 1
Number of weeks = 39
Number of tests given = 31 x 39
Rounding to one significant figure, we get
= 30 x 40
= 1200 tests
So, the total number of tests are 1200.
Problem 8 :
There are 11 biscuits in a pack. Estimate how many biscuits are in a crate containing 138 packs.
Solution :
Number of biscuits in a pack = 11
Number of packs in a crate = 138
Total number of biscuits = 138 x 11
Rounding to one significant figure, we get
= 140 x 11
= 1540 biscuits.
So, total number of biscuits in the crate is 1540.
Problem 9 :
A city car park has 9 floors, each with 79 spaces. Estimate how many parking spaces are there in total.
Solution :
Number of floors = 9
Number of spaces in each floor = 89
Number of parking spaces = 89 x 9
Rounding to one significant figure,
= 90 x 10
= 9000 spaces.
So, the total number of parking spaces is 9000.
Problem 10 :
An avocado tree yields an average of 291 avocados in a season. Estimate the number of avocados that will be harvested from an orchard of 21 trees.
Solution :
Average number of avocados = 291
Total number of trees = 21
Number of avocados harvested = 291 x 21
Rounding to one significant figure,
= 300 x 20
= 6000
So, the total number of avocados harvested is 6000.
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