functional skills mathematics -...

Functional SkillsMathematics

Level 1

Learning Resource 6Decimals

N2/L1.4 N2/L1.5 N2/L1.6 N2/L1.7

DECIMALS LEVEL 1

©West Nottinghamshire College 2

6Excellence in skills development

Contents Read, Write, Order and Compare Decimals N2/L1.4 Pages 3 - 4 Addition and Subtraction of Decimals N2/L1.5 Page 5 Multiplication of Decimals N2/L1.5 Page 6 Division of Decimals N2/L1.5 Pages 7 - 8 Multiply by 10, 100 N2/L1.6 Pages 9 - 10 Divide by 10, 100 N2/L1.6 Pages 11 - 12 Approximate Decimal Places N2/L1.7 Pages 13 - 14 Significant Figures N2/L1.7 Page 15

DECIMALS LEVEL 1

N2/L1.4 6

Excellence in skills development Information Read, Write, Order and Compare Decimals You must always keep the decimal points and figures in their correct columns.

Numbers to the left of the decimal point are whole numbers. Numbers to the right of the decimal point are decimal fractions.

Examples Example 1 Place Value Table


Hundreds 100s

Tens 10s

Units 1s

DecimalPoint

Tenths 10ths

Hundredths 100ths

Thousandths1000ths

5 6 . 2 9 0 . 8 5 1 9 . 6 5 1 4 0 . 0 0 2

56.29 0.851 9.65 140.002 In this table, these numbers have been broken down to show the place value of each digit. The zeros in the numbers given above are known as place holders. Example 2

Put these numbers in order, starting with the largest.

0.34 3.40 0.420 0.125 4.2 Step 1) Arrange all the decimals in a column with the decimal points underneath each

other. Start with the whole numbers 4 . 2 3 . 40

Step 2) Make them all the same length by adding zeros to help with comparison

4 . 2 3 . 40 0 . 420 0 . 340 0 . 125

e.g.

0.42 becomes 0.420 0.34 “ 0.340

DECIMALS LEVEL 1

N2/L1.4



Exercise 1 Read, Write, Order and Compare Decimals 1) Which is the largest?

a) 3.641 2.923 2.120 3.7 2.15

b) 0.503 5.62 6.051 0.96 6.58

c) 0.365 8.15 3.7 0.825 3.82

d) 1.015 0.008 40.03 4.25 8.98

2) Put each group in order, from the cheapest to the most expensive.

a) £5.05 £5.62 £5.30 £0.56 £3.52

b) £19.64 £10.90 £1.90 £109.00 £1.12

c) £4.08 £4.67 £0.41 £0.60 £41.07

d) £6.55 £16.05 £6.05 £16.50 £6.02

3) Draw a place value table (see Example 1). Write the following numbers in it.

a) Sixteen point seven.

b) Five hundred and fifteen point zero two.

c) Three point four two.

d) Eight hundred and forty three point zero zero five.

DECIMALS LEVEL 1

N2/L1.5 6

Excellence in skills development Information Addition and Subtraction of Decimals The calculation needs to be completed as you would do any ordinary addition and subtraction, but remembering to keep the decimal point in line. You must keep the decimal points and figures in their correct columns.

Examples 1.2 2.4 11.47 16.48 2.5 3.7 1.76 2.7 3.7 6.1 13.23 19.18


1 1 1 1 1 1

2 1 7 9 1 2 1

3.9 3.1 8.01 0.430 1.3 1.6 3.27 0.316 2.6 1.5 4.74 0.114 Exercise 2 1) 2.1 2) 3.4 3) 2.01 4) 2.44

1.1 1.4 2.23 2.32 5) 2.7 6) 4.3 7) 3.91 8) 3.83

2.3 3.8 3.74 4.58 9) 25.31 10) 1.64 11) 6.9 12) 7.7 47.24 44.35 2.0 3.2

14.12 32.07 13) 6.8 14) 8.8 15) 9.15 16) 7.68 2.7 4.6 4.04 3.71

+ + + +

- - - -

+++ +

+ +

+ -

-

++

-+

- - -

DECIMALS LEVEL 1

N2/L1.5 6

Excellence in skills development Examples Multiplication of Decimals Example 1 2.6 × 4 Steps:

26 × 4 104

1) Multiply as if using whole numbers.

2) Count the number of figures after the decimal: 2.6 × 4. There is one such figure.

3) Count one place from the right in the answer and place the decimal point.

Answer 10.4

Example 2 9.25 × 7 Steps:

1) Multiply as if using whole numbers. 925 × 7 6475

2) Count the number of figures after the

decimal point in the question : 9.25 × 7 There are two such figures.

3) Count two places from the right in the answer and place the decimal point.

Answer 64.75

E

xercise 3

) 2.1 × 3 2) 1.2 × 4 3) 2.3 × 5

) 3.2 × 6 5) 2.2 × 7 6) 4.2 × 8

) 1.3 × 9 8) 2.6 × 2 9) 3.4 × 4

0) 3.6 × 6 11) 1.8 × 8 12) 3.7 × 3

3) 5.1 × 7 14) 7.1 × 8 15) 2.9 × 7

1

4

7

1

1


DECIMALS LEVEL 1

N2/L1.5 6

Excellence in skills development Examples Division of Decimals Example 1 13.5 ÷ 3 3 13.5 3 into 13.5 3 13.5 3 into 1 doesn’t go 4. 3 into 13 goes 4 times remainder 1 3 13.15 put the 4 above the 3 and carry the 1 put decimal point in above the other decimal point 4. 5 3 into 15 goes five times 3 13.15 put in the 5 Example 2 17.02 ÷ 4 4 17.02 4 into 17.02 4 17.02 4 into 1 doesn’t go 4 17.02 4 in 17 goes 4 times remainder 1 4. Put in the 4 and carry the 1 4 17.1 02 put the decimal point in above the other decimal point 4. 2 4 into 10 goes twice remainder 2 4 17.1 022 put in the 2 and carry the remainder 4. 2 5 4 into 22 goes five times remainder 2 4 17.1 022 put in the 5 We could go on to get a more accurate answer or we could simply give the answer as 4.25 remainder 2.


DECIMALS LEVEL 1

N2/L1.5



Exercise 4 Division of Decimals 1) 4.2 ÷ 3 2) 5.6 ÷ 4 3) 7.5 ÷ 5

4) 8.4 ÷ 6 5) 9.8 ÷ 7 6) 10.4 ÷ 8

7) 11.7 ÷ 9 8) 14.3 ÷ 11 9) 16.8 ÷ 12

10) 0.54 ÷ 3 11) 0.64 ÷ 4 12) 0.85 ÷ 5

13) 0.96 ÷ 6 14) 1.05 ÷ 7 15) 1.44 ÷ 8

16) 1.98 ÷ 9 17) 1.87 ÷ 11 18) 1.92 ÷ 12

Exercise 5 Look back over Exercises 2, 3, and 4 and check your answers are approximately correct by rounding to whole numbers. Examples of this could be:

2.1 + 1.1 = (3.2) Approx. 2 + 1 = 3

2.1 × 3 = (6.3) Approx. 2 × 3 = 6

4.2 ÷ 3 = (1.4) Approx. 4 ÷ 3 = 1

DECIMALS LEVEL 1

N2/L1.6 6

Excellence in skills development Information Multiply by 10, 100 To multiply by 10, move the digits one place to the left. To multiply by 100, move the digits two places to the left. The number of zeros in 10/100 tells you how many places to move the digits. (1 digit for 10, 2 digits for 100). Sometimes you may have to put zeros on the end of the number in order to be able to move the digits the right number of places. Examples Multiplying by 10

2 × 10 = 20

2.3 × 10 = 23 (this could be written as 23.0)

26.3 × 10 = 263

3.62 × 10 = 36.2

The digits move one place to the left. Multiplying by 100

2.3 × 100 = 230.0

5.46 × 100 = 546 (this could be written as 546.0)

6.7 × 100 = 670

289 × 100 = 28,900

The digits move two places to the left.


DECIMALS LEVEL 1

N2/L1.6 6

Excellence in skills development Exercise 6 Multiply by 10, 100 1) 6.5 × 10 2) 2.7 × 10 3) 11.4 × 10

4) 15.8 × 10 5) 32.5 × 10 6) 1.06 × 10

7) 3.05 × 10 8) 4.04 × 100 9) 6.32 × 100

10) 32.5 × 100 11) 91.3 × 100 12) 6.5 × 100

13) 7.8 × 100 14) 3.9 × 100 15) 28.3 × 10

16) Underline the number that is 10 times 24.

2.4 240 204 2400

17) Underline the number that is 100 times 560.

55.60 5600 56,000 5060

18) Put numbers in the boxes to make these statements true. 87 × = 8700

314 × = 31,400

9 × = 90


DECIMALS LEVEL 1

N2/L1.6 6

Excellence in skills development Information Divide by 10, 100 Division is an operation that is like an opposite of multiplying. Mathematicians call this an ‘Inverse Operation’. To divide by 10, move the digits one place to the right. To divide by 100, move the digits two places to the right. The number of zeros in 10/100 tells you how many places to move the digits. (1 digit for 10, 2 digits for 100).

Sometimes you may have to put zeros at the front of the number in order to be able to move the digits the right number of places.

A decimal point should not be used on its own at the front of a number. Remember to use a zero to show there are no whole numbers. In numbers like 6.50, the final zero can be left off to give 6.5 because 0.50 does NOT represent fifty. Examples

12 ÷ 10 = 1.2

37 ÷ 10 = 3.7

61·3 ÷ 10 = 6.13

7.6 ÷ 10 = 0.76

The digits move one place to the right.

165.3 ÷ 100 = 1.653

72.4 ÷ 100 = 0.724

195 ÷ 100 = 1.95

5.00 ÷ 100 = 0.05

The digits move two places to the right.


DECIMALS LEVEL 1

N2/L1.6



Exercise 7 Divide by 10, 100 1) 31.2 ÷ 10 2) 66.3 ÷ 10 3) 27.4 ÷ 10 4) 17.6 ÷ 10 5) 18.63 ÷ 10 6) 9.74 ÷ 10 7) 6.59 ÷ 10 8) 341.6 ÷ 100 9) 743.62 ÷ 100 10) 58.89 ÷ 100 11) 45.26 ÷ 100 12) 28.34 ÷ 100 13) 142 ÷ 100 14) 510.13 ÷ 100 15) 823.17 ÷ 100 16) Underline the number that is 56 divided by 10.

0.56 5600 5.6 560

17) Underline the number that is 829 divided by 100.

82.9 890 8290 8.29

18) Put numbers in the boxes to make these statements true. 359 ÷ = 3.59

7325.5 ÷ = 732.55

244.00 ÷ = 2.44

DECIMALS LEVEL 1

N2/L1.7 6

Excellence in skills development Information Approximate Decimal Places Numbers as answers to questions may need to be approximated to a whole number or a given number of decimal places. This is particularly true when using a calculator. To give an answer to a specific number of decimal places, we look at the next digit to decide whether to round up or down. i.e.

- If this is less than 5 (i.e. 0 to 4), the digit in the second decimal place stays as it is.

- If the third decimal place is 5 or greater, the digit in the second decimal place is increased by one.

Examples Write 36.5823 to 2 decimal places. The third decimal digit is 2, so the second decimal digit stays as it is.

Answer - 36.58 Write 15.87 to 1 decimal place. The second decimal digit is 7, so the first decimal digit is increased by one.

Answer - 15.9 Write 121.654 to 1 decimal place. The second decimal digit is 5, so add one to the first decimal digit.

Answer - 121.7 Write 743.45 to the nearest whole number. The first decimal digit is 4, so the unit number stays as it is. Answer - 743


DECIMALS LEVEL 1

N2/L1.7 6

Excellence in skills development Exercise 8 Approximate Decimal Places Write the following to two decimal places. 1) 5.6322 2) 14.8634 3) 85.249

4) 28.655 5) 12.959 6) 37.962

Write the following to one decimal place. 7) 0.872 8) 1.309 9) 14.3499

10) 124.66 11) 5.972 12) 8.554

Write the following to the nearest whole number. 13) 21.43 14) 7.65 15) 9.81

16) 344.38 17) 43.56 18) 235.74

In the following question, round the values (to whole numbers) and then estimate the answer.

19) Billy has to post 3 parcels. Estimate the total weight of the parcels.

1.55 kg

0.94 kg 2.2 kg


DECIMALS LEVEL 1

N2/L1.7



Information Significant Figures Numbers as answers to questions sometimes need to be approximated to a given number of significant figures. This is particularly true when using a calculator. To write a number to a given number of significant figures is exactly the same as writing to a number of decimal places, except that we need to count all the figures in the number, not just the ones after the decimal point. We always count the significant numbers from the left. Examples Write 24.739 to 4 significant figures. The fourth significant figure is increased by one.

Answer - 24.74 Write 16·045 to 2 significant figures.

Answer - 16 Write 3750.284 to 2 significant figures. The third significant figure is 5, so the second is increased by one, but the decimal point must be in the same place.

Answer - 3800 Exercise 9 Write the following to the given number of significant figures. 1) 2.434 to 3 significant figures

2) 0.05847 to 2 significant figures




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