0.45 = 0 · topic 1: changing fractions to decimals ... 2 = _____ f 0 · ˜ 4 ˜ 3 ... question 1...

$: 0.45 = 0 · Topic 1: Changing fractions to decimals ... 2 = _____ f 0 · ˜ 4 ˜ 3 ... QUESTION 1 Complete the equivalent rates$
Mathletics Instant

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Mathletics Instant

Workbooks

Mathletics Instant

Workbooks

Student Book - Series K-1

Rational Numbers

0.45 = 0.4545. .

Rational numbersStudent Book - Series K

Contents

Topics

Topic 1 - Changing fractions to decimals __/__/__ Date completed

Topic 2 - Changing decimals to fractions __/__/__ Topic 3 - Recurring and repeating decimals __/__/__ Topic 4 - Changing recurring decimals to fractions __/__/__ Topic 5 - Rates __/__/__ Topic 6 - Conversions of rates __/__/__

Topic 8 - Some general number properties __/__/__

Topic 7 - Surds and indices __/__/__

Author of The Topics and Topic Tests: AS Kalra

Practice Tests

Topic 1 - Topic test A __/__/__ Topic 2 - Topic test B __/__/__

Rational numbersMathletics Instant Workbooks – Series K Copyright © 3P Learning

Rational numbers

Rational numbersMathletics Instant Workbooks – Series K Copyright © 3P Learning 1

Topic 1: Changing fractions to decimals

QUESTION 1 Write the following as decimals.a 1

10 = ______________ b 510 = ______________ c 9

10 = ______________

d 3100 = ______________ e 7

100 = ______________ f 11100 = ______________

g 21000 = ______________ h 35

1000 = ______________ i 1631000 = ______________

j 834 = ______________ k 564 = ______________ l 21 = ______________10 000 100 000 1000 000QUESTION 2 Change to decimals.a 6 + 5 = ______________ b 9 + 7 = ______________ c 23 + 18 = ______________10 10 100d 39 + 7 = ______________ e 27 + 3 = ______________ f 91 + 81 = _____________100 100 1000g 29 + 3 = ______________ h 52 + 17 = ______________ i 63 + 13 = _____________1000 100 1000j 83 + 2 = ______________ k 94 + 12 = ______________ l 69 + 35 = ____________100 1000 10 000QUESTION 3 Change each fraction to a decimal.a 3 = ______________ b 12 = ______________ c 15 = ______________10 100 1000d 64 = ______________ e 127 = ______________ f 635 = ______________100 1000 10 000g 5 = ______________ h 3 = ______________ i 9 = ______________8 5 25j 1 = ______________ k 16 = ______________ l 9 = ______________8 125 8QUESTION 4 Express as decimals.a 5 = ______________ b 27 = ______________ c 5 = ______________50 100 25d 364 = ______________ e 72 = ______________ f 58 = ______________100 1000 40g 85 = ______________ h 608 = ______________ i 24 = ______________500 1000 50j 17 = ______________ k 18 = ______________ l 7 = ______________750 125 15QUESTION 5 Write as a decimal.a 24 = ______________ b 638 = ______________ c 539 = ______________10 100 1000d 249 = ______________ e 865 = ______________ f 43 = ______________10 000 100 000 50g 110 = ______________ h 48 = ______________ i 370 = ______________200 500 5000j 19 = ______________ k 36 = ______________ l 563 = ______________40 125 800

CHAPTER 1Rational numbers

UNIT 1: Changing fractions to decimals

Chapter 1: Rational numbers 1

ANSWERS

page 149

Rational numbers


Topic 2: Changing decimals to fractions

QUESTION 1 Write the following terminating decimals as fractions.a 0·3 = ______________ b 0·7 = ______________ c 0·5 = ______________d 0·81 = ______________ e 0·24 = ______________ f 0·38 = ______________g 0·125 = ______________ h 0·575 = ______________ i 0·85 = ______________j 0·545 = ______________ k 0·86 = ______________ l 0·193 = ______________

QUESTION 2 Change to fractions.a 0·02 = ______________ b 0·04 = ______________ c 0·05 = ______________d 0·003 = ______________ e 0·008 = ______________ f 0·025 = ______________g 0·007 = ______________ h 0·005 = ______________ i 0·015 = ______________j 0·805 = ______________ k 0·304 = ______________ l 0·708 = ______________

QUESTION 3 Change each decimal to a mixed numeral.a 1·2 = ______________ b 3·4 = ______________ c 8·9 = ______________d 2·25 = ______________ e 3·64 = ______________ f 5·75 = ______________g 8·3 = ______________ h 9·4 = ______________ i 7·2 = ______________j 6·1 = ______________ k 5·42 = ______________ l 8·93 = ______________

QUESTION 4 Express as a mixed numeral.a 6·125 = ______________ b 8·342 = ______________ c 9·45 = ______________d 10·325 = ______________ e 29·36 = ______________ f 41·175 = ______________g 18·63 = ______________ h 128·48 = ______________ i 526·5 = ______________j 16·801 = ______________ k 19·5 = ______________ l 428·55 = ______________

QUESTION 5 Write as a mixed numeral.a 5·64 = ______________ b 9·235 = ______________ c 60·724 = ______________d 83·75 = ______________ e 83·42 = ______________ f 81·48 = ______________g 94·25 = ______________ h 49·123 = ______________ i 53·231 = ______________j 51·125 = ______________ k 86·514 = ______________ l 32·519 = ______________

Rational numbersUNIT 2: Changing decimals to fractions

2 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1

ANSWERS

page 149

Rational numbers


Topic 3: Recurring and repeating decimals

QUESTION 1 Which of the following are recurring decimals and which are terminating decimals?a 1·38 = ______________ b 0·111 = ______________ c 3·851 = ______________d 0· �3 = ______________ e 8·25 = ______________ f 0·1212 = ______________g 5·8453 = ______________ h 0·3695 = ______________ i 0· �4 �3 = ______________j 0·�7 = ______________ k 5·356 = ______________ l 0·26666... = _____________

QUESTION 2 Write the following recurring decimals in a shorter form.a 0·333 ... = ______________ b 0·4333 ... = ______________ c 0·135135 ... = ____________d 0·777 ... = ______________ e 0·807878 ... = ______________ f 0·23333 ... = ____________g 0·252525 ... = ______________ h 0·363636 ... = ______________ i 0·11111 ... = ____________j 0·505505 ... = ______________ k 0·27777 ... = ______________ l 0·7272 ... = ____________

QUESTION 3 Write the following recurring decimals in an expanded form.a 0·�2 = ______________ b 5·�3 = ______________ c 9·�5 = ______________d 0·�2�3 = ______________ e 0·86�1 = ______________ f 0·4�9�5 = ______________g 0·�5�4 = ______________ h 0· �4�5 = ______________ i 0·2�7 = ______________j 0·7�3 = ______________ k 0·�37�5 = ______________ l 0·25�9�3 = ______________

QUESTION 4 Write down the following as recurring decimals.a 0·666 ... = ______________ b 0·2626 ... = ______________ c 1·555 ... = ____________d 0·2222 ... = ______________ e 0·01515 ... = ______________ f 9·8888 ... = ____________g 5·3636 ... = ______________ h 0·2828 ... = ______________ i 7·9393 ... = ____________j 1·5333 ... = ______________ k 0·111 ... = ______________ l 0·04888 ... = ____________

QUESTION 5 Write the following as recurring decimals.a 0·0555 ... = ______________ b 0·0666 ... = ______________ c 0·2727 ... = ____________d 0·03636 ... = ______________ e 0·8333 ... = ______________ f 0·0111 ... = ____________g 1·222 ... = ______________ h 0·05454 ... = ______________ i 2·777 ... = ____________j 0·727272 ... = ______________ k 0·04848 ... = ______________ l 0·006262 ... = ____________

QUESTION 6 Write the following fractions as recurring decimals.a 2

11 = ______________ b 39 = ______________ c 5

6 = ____________d 7

9 = ______________ e 815 = ______________ f 5

27 = ____________g 8

55 = ______________ h 766 = ______________ i 11

9 = ____________j 25

7 = ______________ k 6313 = ______________ l 6

7 = ____________

Rational numbersUNIT 3: Recurring and repeating decimals


ANSWERS

page 149

Rational numbers


Topic 4: Changing recurring decimals to fractions

QUESTION 1 Write the following recurring decimals as fractions or mixed numbers.

a 0· �3 = ______________ b 0· �7 = ______________ c 0· �5 = ______________

d 0· �5 �4 = ______________ e 0· �7 �2 = ______________ f 0· �4 �3 = ______________

g 0· 5�7 =______________ h 0· �8 = ______________ i 0·3 �4 = ______________

j 0·2�6 = ______________ k 0·72 �6 = ______________ l 0· �2 �3 = _____________

QUESTION 2 Write the following recurring decimals as fractions.

a 0· �1�5 ______________ b 0· �4 = ______________ c 0· �3 �7 = ______________

d 0·0 �8 = ______________ e 0· �6 �3 = ______________ f 0· �12�3 = ______________

g 0·28 �3 = ______________ h 5· �3 = ______________ i 0·2 �2�7 = ______________

j 3·�2�4 = ______________ k 0· �4 �5 = ______________ l 5· �3 �7 = _____________

QUESTION 3 Write the following recurring decimals as fractions in their simplest form.

a 0·00�2 ______________ b 0· �45 �6 ______________ c 5· �5 �8 = ______________

d 1· �3 �1 = ______________ e 7· �6 = ______________ f 0· �8 �1 = ______________

g 4·2 �5 = ______________ h 0·05�8 = ______________ i 2· �8 �2 = ______________

j 0·�2�7= ______________ k 2·0 �1 �3 = ______________ l 0· �34 �5= _____________

Rational numbersUNIT 4: Changing recurring decimals to fractions

4 EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 1

ANSWERS

page 149

Rational numbers


Topic 5: Rates

QUESTION 1 Complete the following sentences.a 1430 km in 13 hours is a rate of ______________________________________ per hour.b Monique works for 28 hours and is paid $268.80 her rate of pay is ______________________ per hour.c Claudette earns $621.25 for a 35 hour week. Her hourly rate of pay is ______________ dollars per hour.d 9·8 kg of meat costs $91.14, which equals _____________________ per kilo.e If 3600 litres of water flows through a tap in 12 hours, it flows at a rate of _______________ per

minute.

QUESTION 2

a Simone drives 490 km in five hours. Find her average speed._____________________________________________________________________________________________________________________________________________________________________________________________________________

b A car travels at the speed of 31 m/s. How many kilometres does it travel in two hours?________________________________________________________________________________________________________________________________________________________________________________________

c A car uses petrol at the rate of 8·25 L/100 km. How many litres would be used to travel 2460 km? _______________________________________________________________________________________________________________________________________________________________________________

QUESTION 3

a Around schools, speed is limited to 40 km/h. A driver is distracted for 5 seconds. What distance does hecover in this time travelling at this speed?_____________________________________________________________________________________________________________________________________________________________________________________________________________________________

b A tap drips at the rate of 3 mL/min. How much water is wasted in a day? ___________________________________________________________________________________________________________________________________________________________________________________________________

Rational numbersUNIT 5: Rates


ANSWERS

page 149

A factory produces 560 bottles each minute. How long does it take to produce 1 000 000 bottles?c

QUESTION 1 Complete the following sentences.a 1430 km in 13 hours is a rate of ______________________________________ per hour.b Monique works for 28 hours and is paid $268.80 her rate of pay is ______________________ per hour.c Claudette earns $621.25 for a 35 hour week. Her hourly rate of pay is ______________ dollars per hour.d 9·8 kg of meat costs $91.14, which equals _____________________ per kilo.e If 3600 litres of water flows through a tap in 12 hours, it flows at a rate of _______________ per

minute.

QUESTION 2

a Simone drives 490 km in five hours. Find her average speed._____________________________________________________________________________________________________________________________________________________________________________________________________________

b A car travels at the speed of 31 m/s. How many kilometres does it travel in two hours?________________________________________________________________________________________________________________________________________________________________________________________

c A car uses petrol at the rate of 8·25 L/100 km. How many litres would be used to travel 2460 km? _______________________________________________________________________________________________________________________________________________________________________________

QUESTION 3

a Around schools, speed is limited to 40 km/h. A driver is distracted for 5 seconds. What distance does hecover in this time travelling at this speed?_____________________________________________________________________________________________________________________________________________________________________________________________________________________________

b A tap drips at the rate of 3 mL/min. How much water is wasted in a day? ___________________________________________________________________________________________________________________________________________________________________________________________________

Rational numbersUNIT 5: Rates


ANSWERS

page 149

Rational numbers


Topic 6: Conversions of rates

QUESTION 1 Complete the equivalent rates.a 80 mL/min = ___________________ mL/h b 1000 mm/s = ___________________ cm/sc 24·5 t/day = ___________________ kg/h d 60 m/min = ___________________ m/he 275 L/min = ___________________ kL/min f 100 L/h = ___________________ L/dayg 120 km/h = ___________________ km/min h $12.50/h = ___________________ $/dayi 27°/min = ____________________ °/s j 90 km/h = ___________________ km/dayk 54 ha/day = ___________________ m2/day l 2·35 m/s = ___________________ cm/min

QUESTION 2 A speed of 58 metres per second is how many:

a metres per minute. __________________________________________________________________________________________________________________________________________________________

b metres per hour. ____________________________________________________________________________________________________________________________________________________________

c kilometres per hour. _________________________________________________________________________________________________________________________________________________________

d kilometres per day. __________________________________________________________________________________________________________________________________________________________

QUESTION 3 A car is travelling at 110 km/h. How many metres does it travel in one minute?__________________________________________________________________________________________________________________________________________________________

QUESTION 4 A flow rate of 45 mL per second is how many:

a mL per minute = _______________________ b mL per hour = __________________________________________________________________ _________________________________________

c L per hour = __________________________ d kL per hour = __________________________________________________________________ _________________________________________

QUESTION 5 Change:

a 96 km/h to m/s ________________________ b 30 m/s to km/h _________________________________________________________________ _________________________________________

c 120 km/h to m/s _______________________ d 72 km/h to m/min _______________________________________________________________ _________________________________________

Rational numbersUNIT 6: Conversion of rates

EXCEL ESSENTIAL SKILLS: YEAR 10 MATHEMATICS REVISION AND EXAM WORKBOOK 16

ANSWERS

page 149

Rational numbers


Topic 7: Surds and indices

QUESTION 1 Complete the following:a i +5 � +5 = _________________________ ii –5 � –5 = _________________________________b i (+7)2 = ___________________________ ii (–7)2 = ___________________________________c i (+2·5)2 = __________________________ ii (–2·5)2 = _________________________________d When two positive numbers are multiplied, the result is always _________________________________.e When two negative numbers are multiplied, the result is always _________________________________.

QUESTION 2 Complete the following:a i +5 � +5 � +5 = _____________________ ii –5 � –5 � –5 = ______________________________b i (+5)3 = ___________________________ ii (–5)3 = ___________________________________c i (+2·5)3 = __________________________ ii (–2·5)3 = _________________________________d The product of five positive numbers is always a ___________________________ number.3 The product of five negative numbers is always a ___________________________ number.

QUESTION 3 Write these surds in index form.a ��73 = __________________ b (��5)4 = __________________ c 3��105 = _________________

d 3��222 = __________________ e (5��18)2 = _________________ f 7��163 = _________________QUESTION 4 Write the following as surds.a 17 = _________________ b (–10) = __________________ c 18 = _________________

d 12 = __________________ e 24 = _________________ f 28 = _________________

QUESTION 5 Use your calculator to evaluate correct to one decimal place.a �196 = __________________ b 3�1728 = _________________ c � 289 = _________________

d 4�625 = __________________ e 5�128 = _________________ f 6�542 = _________________

QUESTION 6 Use your calculator to evaluate correct to three significant figures.a 3�146 = __________________ b 4�238 = _________________ c 7�649 = _________________

d 6�864 = __________________ e �523 = _________________ f 5�988 = _________________QUESTION 7 Simplify:a x � x = ________________ b a � a � a = ____________ c (y )5 = ________________

d (m16) = ________________ e n � n = _________________ f (16a4b4) = _____________QUESTION 8 Use your calculator to find:a 81– = __________________ b 27– = __________________ c 64– = _________________

d 125– = __________________ e 32– = _________________ f 5–24–2 = _________________

Rational numbersUNIT 7: Surds and indices


ANSWERS

page 149

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13

12

12

14

23

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13

35

13

56

56

14

23

13

15

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13

15

Rational numbers


Topic 8: Some general number properties

QUESTION 1

a List the first five even numbers. ___________________________________________________________b How do you know that a number is even? ___________________________________________________c List the first five odd numbers. ____________________________________________________________d How do you know that a number is odd? ___________________________________________________

QUESTION 1 Complete the following.a The sum of two even numbers is an ___________________________ number.b The sum of two odd numbers is an ___________________________ number.c The sum of an odd and an even number is an ___________________________ number.d The product of any odd number and 2 is an ___________________________ number.e The product of an odd and an even number is an ___________________________ number.

QUESTION 3

a Which is the only even prime number? _____________________________________________________b List all the prime numbers less than 20. ____________________________________________________c List all the prime numbers between 50 and 60. _______________________________________________d The quotient of two positive numbers is ____________________________________________________e The product of three negative numbers is ___________________________________________________

QUESTION 4

a All even numbers end in one of five digits. List them: __________________________________________b All odd numbers end in one of five digits. List them:

___________________________________________c What is the next odd number after 9999? ____________________________________________________d What is the next even number after 99 999? __________________________________________________e The product of two odd numbers is an __________________ number.f The product of two even numbers is an __________________ number.g The square of an odd number is an __________________ number.h The square of an even number is an __________________ number.i The difference between two different odd numbers is an __________________ number.j The difference between two different even numbers is an __________________ number.

Rational numbersUNIT 8: Some general number properties


ANSWERS

page 149

TOPIC TEST PART ARational numbersTime allowed: 15 minutes Total marks = 15

1 A car travels 861 km in 1012 hours. Calculate the average speed.

�A 62 km/h �B 72 km/h �C 82 km/h �D 92 km/h

2 Change 150 km/h into m/min.�A 41·�6 m/min �B 2500 m/min �C 9000 m/min �D none of these

3 20 mL per minute equals how many litres per day?�A 1200 L/day �B 72 000 L/day �C 28 800 L/day �D 28·8 L/day

4 A speed of 25 m/s is how many km/h?�A 70 km/h �B 80 km/h �C 90 km/h �D 100 km/h

5 If x is an integer, what will 2x be?�A odd �B even �C either �D neither

6 The product of two odd integers is?�A odd �B even �C either �D neither

7 (212)2 equals:�A 412 �B 41

4 �C 614 �D 612

8 (113)3 equals:

�A 119 �B 210

27 �C 313 �D 31

9

9 (-1)2 – (–1)3 equals:�A 2 �B 1 �C 0 �D –1

10 (–2)3 + (–3)2 equals:�A 1 �B 17 �C –17 �D –1

11 ��7 is closest to:�A 2 �B 2·6 �C 2·64 �D 2·65

12 Which of the following numbers is not a surd?�A ��11 �B ��3 �C ��117 �D –��64

13 Coal is removed from a mine at the rate of 810 tonnes per hour. Express this in kg/s.�A 810 000 kg/s �B 13 500 kg/s �C 225 kg/s �D 3·75 kg/s

14 A car travels 120 km between 4:30 p.m. and 5:15 p.m. What is the average speed in km/h?�A 90 km/h �B 160 km/h �C 80 km/h �D 85 km/h

15 When a tank is 37 full there is 840 L in it. The total capacity of the tank is:

�A 1680 L �B 1960 L �C 3360 L �D 5880 L

Total marks for PART A 15

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1

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1

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1


ANSWERS

page 149

TOPIC TEST PART ARational numbersTime allowed: 15 minutes Total marks = 15

1 A car travels 861 km in 1012 hours. Calculate the average speed.

�A 62 km/h �B 72 km/h �C 82 km/h �D 92 km/h

2 Change 150 km/h into m/min.�A 41·�6 m/min �B 2500 m/min �C 9000 m/min �D none of these

3 20 mL per minute equals how many litres per day?�A 1200 L/day �B 72 000 L/day �C 28 800 L/day �D 28·8 L/day

4 A speed of 25 m/s is how many km/h?�A 70 km/h �B 80 km/h �C 90 km/h �D 100 km/h

5 If x is an integer, what will 2x be?�A odd �B even �C either �D neither

6 The product of two odd integers is?�A odd �B even �C either �D neither

7 (212)2 equals:�A 412 �B 41

4 �C 614 �D 612

8 (113)3 equals:

�A 119 �B 210

27 �C 313 �D 31

9

9 (-1)2 – (–1)3 equals:�A 2 �B 1 �C 0 �D –1

10 (–2)3 + (–3)2 equals:�A 1 �B 17 �C –17 �D –1

11 ��7 is closest to:�A 2 �B 2·6 �C 2·64 �D 2·65

12 Which of the following numbers is not a surd?�A ��11 �B ��3 �C ��117 �D –��64

13 Coal is removed from a mine at the rate of 810 tonnes per hour. Express this in kg/s.�A 810 000 kg/s �B 13 500 kg/s �C 225 kg/s �D 3·75 kg/s

14 A car travels 120 km between 4:30 p.m. and 5:15 p.m. What is the average speed in km/h?�A 90 km/h �B 160 km/h �C 80 km/h �D 85 km/h

15 When a tank is 37 full there is 840 L in it. The total capacity of the tank is:

�A 1680 L �B 1960 L �C 3360 L �D 5880 L

Total marks for PART A 15

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ANSWERS

page 149

Total marks achieved for PART A 15

Rational numbersTopic Test PART A

Marks

9Rational numbers

Mathletics Instant Workbooks – Series K Copyright © 3P Learning

Time allowed: 15 minutes Total marks = 15

Rational numbersTopic Test PART B

10Rational numbers

Mathletics Instant Workbooks – Series K Copyright © 3P Learning

Total marks achieved for PART B 15

Marks

Time allowed: 15 minutes Total marks = 15

Answers

TOPIC TEST PART BRational numbersTime allowed: 15 minutes Total marks = 15

Question 1

a Write 0·28 as a fraction. ___________________________

b Write 0· �2 �3 as a fraction. ___________________________

c A tap drips at the rate of 4 mL/min. How much water iswasted in a day? ___________________________

d Which is larger 0·5 or 0·�5? ___________________________

e Convert 72 km/h to metres per second (m/s). ___________________________

Question 2

a Calculate the value of 3� 241 correct to three decimal places. ___________________________

b Show that (3��8)2 = 3��82. ___________________________

c Write (4��21)7 in index form. ___________________________

d Simplify (49a8b12) . ___________________________

e Simplify 3�343x12y9z6. ___________________________

Question 3

a Write (xy)–2 without a negative index. ___________________________

b If m is an odd integer, write down the next three odd integers. ___________________________

c Is the sum of two consecutive whole numbers odd or even? ___________________________

d Convert 40 m/s to kilometres per hour (km/h). ___________________________

e Light travels at the speed of 3 � 108 m/s. How manykilometres does it travel in three hours? ___________________________

Total marks for PART B 15

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ANSWERS

page 149

12

Answers Marks


Question 1






Question 2


b Show that (3��8)2 = 3��82. ___________________________


d Simplify (49a8b12) . ___________________________

e Simplify 3�343x12y9z6. ___________________________

Question 3







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12

Answers Marks


Question 1






Question 2


b Show that (3��8)2 = 3��82. ___________________________


d Simplify (49a8b12) . ___________________________

e Simplify 3�343x12y9z6. ___________________________

Question 3







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page 149

12

Answers Marks

0.45 = 0 · topic 1: changing fractions to decimals ... 2 = _____ f 0 · ˜ 4 ˜ 3 ... question 1...

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