Page 45 - Mathematics Coursebook

3.8 Estimating and approximating

In questions 5 to 7:
i solve the problem
ii explain what you have worked out
iii check your answer by estimation or using an inverse operation
iv make sure your workings are clear and neatly presented.
5 Daha is training for a bicycle race.
On Monday he cycles 16.6 km and on Wednesday
he cycles 24.8 km.
a What is the total distance he has cycled?
b Daha wants to cycle a total of 70 km every week.
How much further does he have to cycle this week?
6 Aamina is an electrician. She charges $28 an hour.
a It takes Aamina 6.5 hours to do one job. What is the
total amount she charges for this job?
b To do another job she charges a total of $343. How many
hours did this job take her?
7 Hannah writes a recipe book. The recipe book uses 36 sheets of
paper. She wants to produce 75 copies of the book. There are 500
sheets of paper in one pack. How many packs of paper does she need?

Summary

You should now know that: You should be able to:

+ A decimal number always has a decimal point. + Describe the value of each digit in a
+ The digits to the left of the decimal point decimal number.
represent the whole-number part of a decimal + Multiply and divide whole numbers and decimals
number. by 10, 100 and 1000.
+ The digits to the right of the decimal point + Write decimals in order of size from the smallest
represent the fractional part of a decimal number. to the largest.
+ When you multiply a number by 10, 100 or + Round whole numbers to the nearest 10, 100
1000 the digits move to the left one, two or or 1000.
three places. + Round decimals, including measurements, to the
+ When you divide a number by 10, 100 or 1000 the nearest whole number or one decimal place.
digits move to the right one, two or three places. + Add and subtract integers and decimals.
+ It is always a good idea to estimate the answer + Multiply and divide decimals with one or two
to a question before you work it out, so that you places by single-digit numbers.
know whether your answer is realistic or not.
+ Work out estimates or approximate answers
+ To work out an approximate answer, round all to questions.
your numbers to the nearest 10, 100, … before Use inverse operations and estimation to
doing the calculation. +
check working.
+ Checking your work should help you find any
errors before anyone else does.

+ Presenting your work neatly helps you and anyone
else understand what you have done.

44 3 Place value, ordering and rounding