Functional Skills Mathematics - Yola 06... · 2013-10-31 · Mathematics Learning Resource 6 Decimals N2/L2.5 N2/L2.6. ... Exercise 1 Order and Compare Decimals 1) ... i.e. do an

Level 2

Functional SkillsMathematics

Learning Resource 6Decimals

N2/L2.5 N2/L2.6

DECIMALS LEVEL 2

©West Nottinghamshire College 2

6 Excellence in skills development

Contents

Order and Compare Decimals N2/L2.5 Pages 3 - 4 Practical Rounding N2/L2.5 Pages 5 - 6 Addition and Subtraction of Decimals N2/L2.6 Pages 7 - 8 Multiplication of Decimals N2/L2.6 Pages 9 - 10 Division of Decimals N2/L2.6 Pages 11 - 12

DECIMALS LEVEL 2 N2/L2.5



Information Order and Compare Decimals When comparing numbers of any size, you read from the left and look at the value of each individual digit in its place position. If 2 digits have the same value, you move along to the next column and compare those digits. To keep the numbers in their place order, 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. When comparing decimal numbers you may find it useful to make them all the same length by adding zeros to help with comparison. Always put the answer in the same form as the question and double check that you have put the numbers in the correct order, i.e. largest to smallest or smallest to largest. Examples Put the following numbers in order from largest to smallest: 0.12 0.02 0.2 0.07 1.2 2 Rewrite as a list and add zeros Reorder 0.12 2.00 0.02 1.20 0.20 0.20 0.07 0.12 1.20 0.07 2.00 0.02 Answer 2 1.2 0.2 0.12 0.07 0.02 Order the following numbers from smallest to largest: 12.105 12.005 12.015 12.1 12.05 12.01 Rewrite as a list and add zeros Reorder 12.105 12.005 12.005 12.010 12.015 12.015 12.100 12.050 12.050 12.100 12.010 12.105 Answer 12.005 12.01 12.015 12.05 12.1 12.105




Exercise 1 Order and Compare Decimals 1) Zara had to reorganise the stationery cupboard. She decided to arrange the

notebooks in order of size, with the largest at the bottom. Sizes: 12.75 cm 12 cm 12.05 cm 12.2 cm

Enter the sizes on the stack of books.

2) Kitty wanted to put heavier items in a stronger bag. Which 4 of the following would

she select?

0.454 kg 0.412 kg 0.230 kg 0.095 kg 0.85 kg 0.74 kg 0.6 kg 0.09 kg 3) Are these statements true or false?

1.05 m < 1.1 m true/false 107.75 yds > 107.68 yds true/false 1.301 g > 1.5 g true/false 76.005 ml > 76.01 ml true/false 4) These are the results for the 400 m hurdles final at the Beijing Olympics:

Name Periklis Maret Keiron Danny Angelo Bersham L.J. Markino Time 49.96 48.52 47.98 48.3 47.25 48.06 48.42 48.6

a) Who won the event? (fastest time)

b) Who came 7th? 5) The women’s 400 m swimming freestyle final results were:

Lane 1 2 3 4 5 6 7 8 Time 4:04.66 4:05.05 4:03.29 4:03.56 4:03.22 4:03.52 4:03.60 4:11.26

a) Which lane was the winner in? b) What was the third fastest time?




Information Practical Rounding You should always round decimals to the degree of accuracy which suits your purpose. If you divide the length of a piece of wood and the answer is 30.12567 cm, you clearly cannot saw a piece of wood to that accuracy, 30.1 cm is the best you can do. If you are an engineer, however, you may be working on metal parts needing an accuracy of 0.01 mm. If you work out that you need 495 g of flour for a recipe, for practical purposes you would weigh 500 g. If you are a chemist, however, you may be working to an accuracy of 0.01 g. A question may tell you what degree of accuracy to use. Sometimes you have to decide what size of answer is sensible. Use your common sense. The accuracy of an answer depends on the accuracy of the values used to produce it. In general your answer should have the same number of decimal places as the least precise value used to produce it. Examples What is the area of a room which measures 4.75 metres by 3.7 metres? 4.75 x 3.7 = 17.575 This would be rounded to 1 decimal place as the least precise value (3.7) has only 1 decimal place. To round a number to 1 decimal place, look at the 2nd decimal place. As this figure is greater than 5, add 1 to the first decimal place.

The area of the room is 17.6 m2. What is 4763.982 x 3542.76596? 4763.982 x 3542.76596 = 16877673.26365272 The least precise value in the question has 3 decimal places, so the answer would be rounded to 3 decimal places. To round a number to 3 decimal places, look at the 4th decimal place. As this figure is greater than 5, add 1 to the third decimal place. This gives the answer as 16877673.264 to 3 d.p.




Exercise 2 Practical Rounding 1) Round each of these numbers to: 1 decimal place 2 decimal places 3 decimal places

a) 0.1634 b) 3.6451 c) 23.92551

2) A recipe for 8 showed 1.75 kg of plain flour. Theo used a calculator and worked out that he will need to use 1.3125 kg for 6 people? How much flour should he weigh? (Round to 1 decimal place.)

1.3125 = __________ kg 3) In a race the time is measured in seconds, to 2 decimal places. Which of the

following times wins the race? 54.5673 54.5649 4) Round the following numbers to 3 decimal places and put in order from lowest to

highest. 12.0932 million 12.1049 million 12.0937 million 12.0972 million _____________ _____________ _____________ _____________ 5) The total cost of a buffet lunch for 18 people is £127.60.

Miley tries to work out how much it will cost each for person. Her calculator shows 7.088888888888888888888888888889 How much will each person need to pay? £________




Information Addition and Subtraction of Decimals To add or subtract decimals, write down the numbers in columns with the decimal points lined up then add zeros so that the numbers are all the same length. Do the calculation as you would any ordinary addition and subtraction, remembering to put the decimal point in line in the answer. Examples

100.1 + 40.92 + 6.125 100.100 40.920 + 6.125 147.145

120.007 – 93.09 120.007 - 93.090 26.917 Keira is packing for her holidays. She is allowed 15 kg in her case and a further 10 kg hand luggage. So far her case weighs 13.5 kg and her hand luggage 6.175 kg but she has several more items still to pack. Her extra items weigh 5.8 kg. What weight of items will she not be able to pack? Work out how much extra weight she can pack in her hand luggage and suitcase and add them together. Hand luggage Suitcase 10.000 15.0 3.825 -6.175 - 13.5 1.500 3.825 kg 1.5 kg 5.325 Subtract the extra weight she can put in her suitcase and hand luggage from the weight of extra items: 5.800 - 5.325 0.475 kg She must leave 0.475 kg behind. Another way, or a check that you are correct, would be to add all the weights together: 13.5 + 6.175 + 5.8 = 25.475 kg. This is 0.475 kg over the weight allowance.

1642.7 – 185.019 1642.700 - 185.019 1457.681




Exercise 3 Addition and Subtraction of Decimals 1) 4.619 17.007 3.04 + 3.64_ 6.45 0.1 + 1.264 + 2.408 2) 43.941 0.42 5.1 - 25.82 - 0.228 - 4.982 3) 14.716 + 61.32 = 12.65 + 1.984 = 4.033 + 10.68 = 4) 17.589 - 8.147 = 12.784 - 9.94 = 9.51 - 7.319 = 5) Ava has three lengths of material which she has measured as 1.57 m, 3.2 m and

6.08 m. What is the total length of material? ________ m 6) Louis is checking the price of the digital camera that he wants to buy. The lowest

price is £179.99 plus £5 postage and packaging. The highest price is £196.19 (incl p+p). If he buys the cheaper camera, how much will he save?

£________ 7) Max is measuring the amount of liquid in 5 tanks. All measurements are in litres.

Tank 1 Tank 2 Tank 3 Tank 4 Tank 5 15.136 26.24 7.008 21.983 16.02

What is the total amount of liquid in the tanks? ________ litres




Information Multiplication of Decimals To multiply decimals, you simply multiply as if the numbers were whole numbers (ignoring the decimal points). Use your favourite method to multiply the figures and then put the decimal point in at the end of the calculation. The answer has the same number of decimal places as the 2 original numbers combined. It is always useful to check the result by working out what you would expect the answer to be close to, i.e. do an approximate calculation using whole numbers to make sure that you are likely to be correct. Examples Example 1 9.453 × 7 9453 × 7 66171 There are 3 decimal places in the original sum, so the answer is 66.171 Check: 10 x 7 = 70. 70 is close to the answer of 66, so it is likely to be the correct answer. Example 2 6.35 × 8.5 Multiply as if using whole numbers. Starting with left-hand figure Starting with right-hand figure 635 635 × 85 × 85 50800 3175 3175 50800 53975 53975

There are three decimal places in total in the original sum: 6.35 × 8.5 so the answer is 5 3 . 9 7 5

Check: 6 x 9 = 54. 54 is close to the answer of 53, so it is likely to be the correct answer.




4.5 cm

Exercise 4 Multiplication of Decimals 1) 7.16 × 2

3.612 × 6 12.541 × 4

2) 5.4 × 1.2

19.1 × 7.3 5.7 × 11.4

3) 6.12 × 0.3

5.412 × 0.6 6.132 x 1.35

In questions 4 - 6, make sure you round your answers to a sensible degree of accuracy. 4) Heidi buys 8 boxes of chocolates as presents. If each box costs £4.75, how much

will Heidi spend? £________ 5) Area = length x width. What is the area of a room which is 4.6 m long by 3.75 m

wide? ________ m2

6) Volume of a cuboid = length x width x height. What is the volume of the cuboid shown? ________ cm3 7) You will need to use a calculator for this question.

Volume of a cylinder = π r2 x l π = 3.14 r = radius l = length Calculate the volume of each of the following cylinders to 2 d.p. a) radius 3.75 m, length 5.55 m. ________ m3

b) radius 16.08 cm, length 40.75 cm ________ cm3

c) radius 0.5687 cm, length 5.5 cm ________ cm3

1.7 cm

2.58 cm




Information Division of Decimals In order to divide decimals, the divisor (the number you are dividing by), needs to be a whole number. If it isn’t already a whole number then you multiply both the divisor and the divident (the number you are dividing into) by 10, 100 or 1000 to make it a whole number. You must be sure to multiply the number you are dividing by, and the number you are dividing into, by the same number. When the divisor is a whole number, continue as a normal division, keeping the decimal point in line in your answer. Examples Example 1

14.021 ÷ 7

2.003 7 14.021 Example 2

3.02 ÷ 0.2 becomes 30.2 ÷ 2 15.1 2 30.2 Example 3 1.7283 ÷ 0.003 becomes 1728.3 ÷ 3 5 7 6.1 3 172218.3

[3.02 × 10 = 30.2] [0.2 × 10 = 2]

To make 0.003 a whole number, you must multiply by 1000. [0.003 × 1000 = 3] You must then multiply 1.7283 by 1000. [1.7283 × 1000 = 1728.3]




Exercise 5 Division of Decimals 1) 0.138 ÷ 6

0.133 ÷ 7 0.216 ÷ 9

2) 64.892 ÷ 4

2.59 ÷ 5 0.876 ÷ 8

3) 31.2 ÷ 0.3

748.8 ÷ 0.6 1.9 ÷ 0.5

4) 16.34 ÷ 0.02 2.5131 ÷ 0.03

16.5 ÷ 0.11

5) 12.906 ÷ 0.003

0.46 ÷ 0.023 104.4 ÷ 0.0009

6) Ninety people have won the lottery and £25,250.40 is to be divided between them. How much will each person receive? £________ 7) Fergus has to mark out a field in 1.6 metre lengths. The field measures 24 metres. How many lengths will he mark out? ______ lengths 8) Janey needs £15 to buy her little brother’s birthday present. If she can save £0.75 out of her pocket money each week, how long will she need to save up to buy the present? ______ weeks 9) The exchange rate is 1.6 euros = £1. Corey took 181.20 euro to the U.K. How much is this in £ sterling? £________

Documents

Functional Skills Mathematics - Yola 06... · 2013-10-31 · Mathematics Learning Resource 6 Decimals N2/L2.5 N2/L2.6. ... Exercise 1 Order and Compare Decimals 1) ... i.e. do an