1 A review of relevant calculations

In this chapter, a list of mathematical terms is followed by a diagnostic test. This test is designed to pinpoint those areas of your arithmetic that need revising before you start nursing calculations. The test identifies what you already understand and what you need to review.

You should attempt all questions in the diagnostic test.

Answers are provided in Chapter 7. According to the incorrect answers in your test you will be directed to particular review exercises.

For example, if you make an error in answering either test question 1 or test question 2, then you will be directed to do Review exercise 1A. Or, if your answer to test question 3 or 4 is wrong, you should do Review exercise 1B. You will not need to review any skills that the test shows you already know.

Remember that this test is designed to help you.

Refer to Inside front cover page for explanations of abbreviations.

Diagnostic test

1 Multiply

a 83 × 10

b 83 × 100

c 83 × 1000

2 Multiply

a 0.0258 × 10

b 0.0258 × 100

c 0.0258 × 1000

3 Divide. Write answers as decimals.

a 3.78 ÷ 10

b 3.78 ÷ 100

c 3.78 ÷ 1000

4 Divide. Write answers as decimals.

a

b

c

5 Complete

a 1 kilogram =………………….. grams

b 1 gram =………………….. milligrams

c 1 milligram =………………….. micrograms

d 1 litre =………………….. millilitres

Write answers to 6, 7, 8 and 9 in decimal form.

6

a Change 0.83 kg to grams.

b Change 6400 g to kilograms.

7

a Change 0.78 grams to milligrams.

b Change 34 milligrams to grams.

8

a Change 0.086 milligrams to micrograms.

b Change 294 micrograms to milligrams.

9

a Change 2.4 litres to millilitres.

b Change 965 millilitres to litres.

10

a Change 0.07 L to mL.

b Change 0.007 L to mL.

c Which is larger: 0.07 L or 0.007 L?

11

a Convert 0.045 g to mg.

b Convert 0.45 g to mg.

c Which is heavier: 0.045 g or 0.45 g?

12 Multiply

a 9 × 3

b 0.9 × 3

c 0.9 × 0.3

d 0.09 × 0.03

13 Multiply

a 78 × 6

b 7.8 × 0.6

c 0.78 × 6

d 7.8 × 0.06

14 Which of the numbers 2, 3, 4, 5, 6, 10, 12 are factors of 48?

15 Which of the numbers 2, 3, 5, 6, 7, 9, 11 are factors of 126?

16 Simplify (‘cancel down’)

a

b

17 Simplify

a

b

18 Simplify

a

b

c

19 Simplify

a

b

c

20 Simplify (‘cancel down’). Leave answers as improper fractions.

a

b

c

21 Simplify (‘cancel down’). Leave answers as improper fractions.

a

b

c

22 Simplify. Leave answers as improper fractions, where these occur.

a

b

c

d

23 Round off each number correct to one decimal place.

a 0.68

b 1.82

c 0.35

24 Write each number correct to two decimal places.

a 0.374

b 2.625

c 0.516

25 Change to exact decimal equivalents.

a

b

c

d

26 Change to decimals correct to one decimal place.

a

b

c

27 Change to decimals correct to two decimal places.

a

b

28 Divide. Calculate the value of each fraction to the nearest whole number.

a

b

29 Divide. Calculate the value of each fraction correct to one decimal place.

a

b

30 Change to mixed numbers.

a

b

c

31 Change to improper fractions.

a

b

c

32 Multiply. Simplify where possible.

a

b

c

33 Multiply. Simplify where possible. Write each answer as a fraction, a mixed number, or a whole number.

a

b

34 Multiply. Give each answer as a decimal number.

a

b

Check your answers on page 137–138.

Multiplication by 10, 100 and 1000

To multiply by 10, move the decimal point 1 place to the right.

To multiply by 100, move the decimal point 2 places to the right.

To multiply by 1000, move the decimal point 3 places to the right.

Examples

i 0.36 × 10 0.36 × 10 = = 3.6

ii 0.36 × 100 0.36 × 100 = = 36

iii 0.36 × 1000 0.36 × 1000 = = 360

Notes

• Use zeros to make up places, where necessary.

• If the answer is a whole number, the decimal point may be omitted.

To multiply by	Move the decimal point
10	1 place right
100	2 places right
1000	3 places right

Review exercise 1A

Multiply

1 0.68 × 10 0.68 × 100 0.68 × 1000	9 0.0147 × 10 0.0147 × 100 0.0147 × 1000
2 0.975 × 10 0.975 × 100 0.975 × 1000	10 0.006 × 10 0.006 × 100 0.006 × 1000
3 3.7 × 10 3.7 × 100 3.7 × 1000	11 3.76 × 10 3.76 × 100 3.76 × 1000
4 5.62 × 10 5.62 × 100 5.62 × 1000	12 0.639 × 10 0.639 × 100 0.639 × 1000
5 77 × 10 77 × 100 77 × 1000	13 0.075 × 10 0.075 × 100 0.075 × 1000
6 825 × 10 825 × 100 825 × 1000	14 0.08 × 10 0.08 × 100 0.08 × 1000
7 0.2 × 10 0.2 × 100 0.2 × 1000	15 0.003 × 10 0.003 × 100 0.003 × 1000
8 0.046 × 10 0.046 × 100 0.046 × 1000	16 0.0505 × 10 0.0505 × 100 0.0505 × 1000

Check your answers on page 138.

Division by 10, 100 and 1000

To divide by 10, move the decimal point 1 place to the left.

To divide by 100, move the decimal point 2 places to the left.

To divide by 1000, move the decimal point 3 places to the left.

Example A

i 37.8 ÷ 10 i 37.8 ÷ 10 =

ii 37.8 ÷ 100 ii 37.8 ÷ 100 =

iii 37.8 ÷ 1000 iii 37.8 ÷ 1000 =

Notes

• Use zeros to make up places, where necessary.

• For numbers less than one, write a zero before the decimal point.

Example B

A division may be written as a fraction.

Evaluate i	i
ii	ii
iii	iii

To divide by	Move the decimal point
10	1 place left
100	2 places left
1000	3 places left

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