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Cambridge Lower Secondary Mathematics Workbook 8 2nd Edition Lynn Byrd, Greg Byrd, Chris Pearce - Solutions

7 Work these out. b 0.3x5 0.5-12 e 0.9x-8 All the answers are in the cloud. a -60.04 b -120.2 -0.024 -24 -2.4 -0.24 c -240.001 d -8000.03
6 Work out a 0.1x-9 d 0.7x6
5 To multiply a number by 0.03 divide the number by 100, then multiply by 3 OR multiply the number by 3, then divide by 100. Copy and complete the workings a 5000.03 500-100-5 and 53= b -700 x 0.03 -700 and 3= x3: C 120.03 123-36 and 36-100= d -3x0.03 -33 and -0
4 To multiply a number by 0.02 divide the number by 100, then multiply by 2 OR··multiply the number by 2, then divide by 100.Copy and complete the workings.500×0.02 500+100=5 and 5×2=a b-600×0.02-600+× 2==and 25×0.02 25×2=50 and 50+100=c d-4×0.02-4×2=and
3 To multiply a number by 0.3 divide the number by 10, then multiply by 3 OR multiply the number by 3, then divide by 10. Copy and complete the workings. 30 10 3 and 3 = -50 -50= and a 300.3 b -500.3 C 15x0.3 d -90.3 -9x3= and 3 =[ 15x3=45 and 45+10= F
2 To multiply a number by 0.2 divide the number by 10, then multiply by 2 OR multiply the number by 2, then divide by 10. Copy and complete the workings. 30 10 3 and 3x2= -40 and x2= a 300.2 b -400.2 C 120.2 d -80.2 -82 = and =[ 122 24 and 10 =
1 Look at these rules. x0.2 is the same as 10 and x2 OR 2 and 10 x0.3 is the same as +10 and x3 OR X3 and 10 Follow the pattern to complete these rules. a 0.4 is the same as +10 and x OR b OR and10 x0.6 is the same as +10 and and10
15 The formula to convert a temperature in degrees Centigrade (C) to degrees Fahrenheit (F) is F=C×1.8+32 Use a calculator to work out F when C =- 38.6 ab Which is colder, a temperature of -38.6℃ or -38.6ºF?Explain your answer.
14 y is a number with two decimal places, and -1.43 ≤ y
13 Each card describes a sequence of decimal numbers.A First term: - 7.5 Term-to-term rule: 'add 0.3'B First term: - 1.71 Term-to-term rule: 'multiply by 2'C First term: - 9.95 Term-to-term rule: 'add 1.5'Work out the third term of each sequence.a bWrite the numbers from part a in order of size,
12 Frank and Sarina run around a park every day. They keep a record of the distances they run each day for 10 days. These are the distances Frank runs each day. 400 m 2.4km 0.8 km 3200m 1.6km 32 km 1.2km 2000m 3.6km 1200m a Which distance do you think Frank has written down incorrectly? Explain
11 Write these decimal numbers in order of size, starting with the smallest. a -8.34,-8.06, -8.28, -8.8 b -1.425, -1.78, -1.03, -1.5
10 Write the correct sign, , between each pair of numbers. a -2.3-2.4 C -0.15 -0.08 b -7.23 -7.23 -7.29 d -11.02 -11.5
9 Write the measurements in each set in order of size, starting with the smallest. a 4.3 cm, 27 mm, 0.2 cm, 7mm b 34.5cm, 500 mm, 29 cm, 19.5mm C 2000 g, 75.75 kg, 5550g, 3kg d e f 1.75 kg, 1975 g, 0.9 kg, 1800 g 0.125g, 100 mg, 0.2g, 150 mg 25 km, 2750 m, 0.05 km, 999 m
8 Write the correct sign, < or>, between each pair of numbers. a 9.1 9.03 b 56.4 56.35 C 0.66 0.606 d 3.505 3.7 e 0.77t 806 kg f 7800m 0.8 km g 3.5kg 375g h 156.3 cm 1234 mm
7 Write the correct sign,=or +, between each pair of measurements. a 205.5cm 255mm b 0.125g C 500 g 0.05 kg d 10.5t 125 mg 1050 kg e 0.22 kg 220g f 1.75 km 175m
6 Write the decimal numbers in each set in order of size, starting with the smallest.45.454, 45.545, 45.399, 45,933 ab 5.183, 5.077, 5.044, 5.009 31.425, 31.148, 31.41, 31.14 C7.502, 7.052, 7.02, 7.2 d
5 Write the correct sign, < or>, between each pair of measurements. Copy and complete the working. a 3.5g 380 mg b 0.4t 845 kg 0.4t=0.41000 3.5g 3.5x1000=3500 mg kg 3500 mg 380 mg kg 845 kg C 2.5cm 48 mm 2.5 cm 2.5x10=mm mm 48 mm d 950g 0.08 kg 0.08 kg=0.08 1000 = g 950g g e 2500m 1.9 km 1.9 km
4 Write the correct sign, , between each pair of numbers. Use the number line to help you.20 a -5.2 -5.7 b -6.5 -6.2 C -7.2 -7.5 P -8.8 -8.9 -7 -6 a-5.7 -5.2
3 Write the correct sign, < or >, between each pair Write the correct sign, of numbers.3 7.23 7.27 b9.71 9.83 a20.17 20.09 d3.65 3.9 c
2 Use the same method as in Question 1 to write these decimal numbers in order of size, starting with the smallest. C a 4.29, 4.16, 4.95, 4.91 Write the decimal parts only: Write in order the decimal parts only: Write the complete numbers in order: b 8.94, 8.49, 8.95, 8.47 Write the decimal parts
1 Complete the workings to write these numbers in order of size, starting with the smallest.5.51 5.08 5.21 5.17 All the numbers have the same whole number part, so you only need to compare the decimal parts.Step 1: Write the decimal parts only:51, 08, 21, 17 Step 2: Now write in order the decimal
18 Complete these steps for each calculation. i ii Work out an estimate of the answer by rounding each number to one significant figure. Use a calculator to work out the accurate answer. Give this answer correct to three significant figures (3 s.f.). iii Compare your estimate with the accurate
17 This formula is often used in science. v=u+at Work out the value of a when v=5.2, u=1.4 and 1=72. Round your answer to an appropriate degree of accuracy.
16 A football club sells, on average, 23 000 tickets per match. In one season they play, on average, 46 matches. How many tickets do they sell, on average, each season? Round your answer to an appropriate degree of accuracy.
15 Gerry's electric toothbrush rotates the brush 125 times per second. Gerry brushes her teeth for two minutes, twice a day. How many rotations does her electric toothbrush make in one week? Give your answer correct to one significant figure (1 s.f.).
14 The instructions on a packet of rice say you should cook 75 g per person. Yuang carefully weighed out 75 g of rice. He counted the grains and found he had 2896 grains of rice. Work out the average (mean) mass of a single grain of rice. Give your answer correct to three significant figures (3
13 Round the number 530.403977 to the stated number of significant figures (s.f.). a 1 s.f. d 4 s.f. b 2 s.f. e 5 s.f. 3 s.f. f 6 s.f.
12 Gina drove from her house in Madrid to a friend's house in Paris, a distance of 1275.3 km. Gina then drove to another friend's house in Rome, a distance of 1445.2km. How far did Gina drive altogether? Give your answer correct to two significant figures (2 s.f.).
11 a Use a calculator to work out the answer to 7 Write all the numbers on your calculator display. Round your answer to part a to the stated number of significant figures (s.f.). b i 1 s.f. iv 4 s.f. ii 2 s.f. v 5 s.f. vi S. E 3 s.f. 6 s.f.
10 Which is the correct answer in each case, A, B, C or D?567 rounded to I s.f.a A 5 B6 C 500 D600 b15.493 rounded to 2 s.f.A 15 B16 C15.49 D15.50 0.07887 rounded to 3 s.f.U A 0.078 B0.079 0.0789 D0.0790 0.007 777 77 rounded to 4 s.f.P A0.0077 B0.0078 C0.007777 D0.007 778 0.039.63 rounded to 2
9 Round each number to the given number of significant figures (s.f.).2468.15 (1 s.f.)b 759.233 (2 s.f.)5.3691 (3 s.f.)a c0.0781 (1 s.f.)0.1954 (2 s.f.)f 6.038 88 (3 s.f.)d e0.899 (2 s.f.)964 (1 s.f.)h 19.985 (3 s.f.)i g
8 This is part of Li's homework. Question Round each number to 3 s.f. a 2374650 Answer a 237 b 0.002058 84 b 0.002 Li has rounded one large number and one small number to three significant figures. Both answers are wrong. Explain the mistakes Li has made. a b Write the correct answers.
7 Round each number to two significant figures (2 s.f.). All the answers are in the circle. a 358 d 0.003 5601 b 0.361 e 35.99 C 3572 f 3.6009
6 Round each number to one significant figure (1 s.f.).Choose the correct answer: A, B or C.500 468 A5 B50 Ca 9.02 10 0.9 Cb AB 95686 5000 A6000 BC 6c 0.0035 dA 4B 0.04 C0.004
5 a 0.0231 b 0.005 671 0.0000381 d 0.688 C 0.000038 1 d 0.688
4 Use Paolo's method to round each number to 1 significant figure. b 0.005671 C Round each number to 2 significant figures. a 0.0231
3 Round each number to 3 significant figures. 3 a 4729 b 66549 C 2355244 Paolo uses this method to round 0.002432 to 1 significant figure. Draw a line after the first s.f. and circle the next digit. The circled digit is a 4, so leave the 2 as it is. Do not write the 4, 3 or 2 but remember to write
2. Round each number to 2 significant figures.a 213 b 4823 C 23850 d 185255
1 Use Erin's method to round each number to 1 significant figure.4823 185255 ba 23 850 d213 C
16 This is part of Ceri's homework.Question'When you multiply a number with one decimal place by 0.01 you will always get an answer smaller than zero."Write one example to show this statement is not true.Answer 345.8×0.01 = 3.458 and 3.458 is not smaller than zero so the statement is not true.For
15 Alicia thinks of a number.Alicia divides her number by 0.01, and then multiplies the answer by 0.1.Alicia then divides this answer by 0.01 and gets a final answer of 2340.What number does Alicia think of first?Explain how you worked out your answer.
14 The diagram shows a triangle of height 0.1 m.The area of the triangle is 1.16m2.The formula for the area of a triangle is A= - bh 2a Rearrange the formula to make b the subject.b Use your formula to work out the base length of the triangle. 0.1 m base
13 A tiler works out the area of the wall he is going to tile.The tiler uses this formula to work out the extra area of tiles he must order due to wastage.E=0.1.4 where:E is the extra area A is the area of the wall The diagram shows the dimensions of the wall he is going to tile.0.6 m 2 m aWork out
12 Which calculation, A, B, C or D, gives a different answer to the other three?Show your working.A 0.096-0.1 B96×0.01 C 9.6x0.1 D 96+0.01
11 What goes in the box. 0.1 or 0.017 44×=4.4 b4.4+=44 0.40x=0.004 a€d 4+=40 44.4x=0.444 f44+=4400 e
10 Which symbol. Xor +, goes in each box?0.1=550 a55 b46 0.01 = 0.46 c3.7 0.1=37 d208 0.01= 2.08 f0.01=5.05 e0.19 0.1=1.9 505
9 Work out the answers to these questions.Use inverse operations to check your answers.27.9×0.01 2.7+0.01 27×0.1 b0.2+0.1 ad
8 Work out 5+0.1 b5.6+0.1 55.6+0.1 d0.55=0.1 aU 5+0.01 f5.6+0.01 55.6+0.01 h0.55+0.01 eg
7 Work out 33×0.1 30×0.1 8.7×0.1 ab 999×0.1 cd 77×0.01 70×0.01 f700×0.01 h7×0.01℮g
6 Work out these.1.6 16 160 1600 All the answers are in the rectangle.16+0.1 b0.16+0.1 a0.16+0.01 d16-0.01 c
5 Copy and complete the workings.2+0.01=2×100=5+0.01=5x ba 30=0.01=30×d 12-0.01=12x c==
4 Copy and complete the workings.4+0.1=4×10=b 7+0.1=7x a=20=0.1=20×25+0.1=25x c=d 11+0.01 is the same as ×100 e.g.6=0.01=6×100=600
3 Work out these.0.12 1.2 12 120 All the answers are in the rectangle.120×0.1 12×0.1 ab 12000×0.01 cd 12×0.01+0.1 is the same as ×10 e.g. 6+0.1=6×10=60
2 Copy and complete the workings.300×0.01=300=100=b 500×0.01=500+a 800×0.01=800+650×0.01=650+c=d=
1 Copy and complete the workings.20×0.1=20=10=b 70×0.1=70=a=80×0.1=80+d 75×0.1=75+C==×0.01 is the same as +100 e.g. 600 × 0.01 = 600- 100=6-
8 Here are five calculation cards.a Work out the answer to each calculation.b Write the answers in order of size, starting with the smallest. A -240.52 C EL 0.03x-430 0.9x-15 B 0.07x-180 D -200.65
7 Work these out. All the answers are in the cloud. -60.04 a C -24 0.001 b -120.2 d -8000.03-0.024 -24 -2.4 -0.24
6 Work out a 0.1x-9 b 0.3 5 C 0.512 d 0.76 e 0.9x-8
5 To multiply a number by 0.03 divide the number by 100, then multiply by 3 OR multiply the number by 3, then divide by 100. Copy and complete the workings. 500-100-5 and 53=[ a 5000.03 b -7000.03 -700 and3= C 120.03 123 36 and 36 100: = d -3 0.03 -33 and +=
4 To multiply a number by 0.02 divide the number by 100, then multiply by 2 OR.·multiply the number by 2, then divide by 100.Copy and complete the workings.500×0.02 500+100=5 and 5×2=a b-600×0.02-600+× 2==and 25×0.02 25×2=50 and 50=100=C d-4×0.02-4×2=and=
3 To multiply a number by 0.3 divide the number by 10, then multiply by 3 OR··multiply the number by 3, then divide by 10.Copy and complete the workings.30×0.3 30+ 10=3 and× 3=a b-50×0.3-50+11 and×3=15×0.3 15×3=45 and 45+10=C d-9×0.3-9×3=and+=
2 To multiply a number by 0.2 divide the number by 10, then multiply by 2 OR multiply the number by 2, then divide by 10. Copy and complete the workings.a 300.2 b -400.2 120.2 d -80.2 30 10 3 and 32=| -40 12x2=24 and and [ x2= +10: -82 = and C +
1 Look at these rules.Follow the pattern to complete these rules.x0.4 is the same as + 10 and X a OR X and =10 b x0.6 is the same as + 10 and X and =10 OR x x0.2 is the same as +10 and x2 OR 2 and 10 x0.3 is the same as +10 and x3 OR X3 and10
13 Each card describes a sequence of decimal numbers.A First term: - 7.5 Term-to-term rule: 'add 0.3"First term: - 1.71 BTerm-to-term rule: 'multiply by 2'C First term: - 9.95 Term-to-term rule: 'add 1.5'a Work out the third term of each sequence.b Write the numbers from part a in order of size,
12 Frank and Sarina run around a park every day. They keep a record of the distances they run each day for 10 days. These are the distances Frank runs each day. 400 m 2.4km 0.8 km 3200m 32km 1.2km a 1.6km 2000m 3.6km 1200m Which distance do you think Frank has written down incorrectly? Explain your
11 Write these decimal numbers in order of size, starting with the smallest. a -8.34,-8.06, -8.28, -8.8 b -1.425, -1.78, -1.03, -1.5
10 Write the correct sign, < or>, between each pair of numbers. a C -2.3-2.4 -0.15-0.08 b -7.23 -7.23 -7.29 d -11.02 -11.5
9 Write the measurements in each set in order of size, starting with the smallest. a b C d e f 4.3 cm, 27 mm, 0.2 cm, 7mm 34.5cm, 500mm, 29 cm, 19.5mm 2000 g, 75.75 kg, 5550 g, 3kg 1.75 kg, 1975 g, 0.9 kg, 1800g 0.125 g, 100 mg, 0.2 g, 150 mg 25 km, 2750 m, 0.05 km, 999 m
8 Write the correct sign, < or >, between each pair of numbers.9.1 9.03 b56.4 56.35 a0.606 0.66 d3.505 3.7 C0.77t 806 kg f7800 m 0.8 km e375 g 3.5kg h156.3cm 1234 mm g
7 Write the correct sign, = or #, between each pair of measurements.205.5cm 255 mm b0.125g 125 mg a500 g 0.05kg d10.5t 1050 kg c0.22 kg 220 g f1.75 km 175 m e
6 Write the decimal numbers in each set in order of size, starting with the smallest.45.454, 45.545, 45.399, 45.933 ab 5.183, 5.077, 5.044, 5.009 31.425, 31.148, 31.41, 31.14 c7.502, 7.052, 7.02, 7.2 d
5 Write the correct sign, < or >, between each pair of measurements Copy and complete the working.380 mg 3.5 g 3.5g=3.5×1000=3500 mg 3500 mg 380 mg ab 0.4t 845kg 0.4t=0.4× 1000=kg kg 845 kg 2.5cm 48 mm 2.5cm=2.5×10=c mm 48 mm mm 0.08 kg d950 g 0.08 kg=0.08 × 1000 950 g g2500 m 1.9 km
4 Write the correct sign, , between each pair of numbers. Use the number line to help you.a -5.2 -5.7 b -6.5 -6.2 C -7.2 -7.5 d -8.8 -8.9 -8 -7 6 a-5.7 -5.2
3 Write the correct sign, < or>, between each pair of numbers. a 7.27 7.23 C 20.17 20.09 b 9.71 9.83 d 3.9 3.65
2 Use the same method as in Question 1 to write these decimal numbers in order of size, starting with the smallest. a 4.29, 4.16, 4.95, 4.91 b Write the decimal parts only: Write in order the decimal parts only: Write the complete numbers in order: 8.94, 8.49, 8.95, 8.47 Write the decimal parts
1 Complete the workings to write these numbers in order of size, starting with the smallest. 5.51 5.08 5.21 5.17 All the numbers have the same whole number part, so you only need to compare the decimal parts. Step 1: Write the decimal parts only: Step 2: Now write in order the decimal parts only:
18 Complete these steps for each calculation. i Work out an estimate of the answer by rounding each number to one significant figure. ii Use a calculator to work out the accurate answer. Give this answer correct to three significant figures (3 s.f.). iii Compare your estimate with the accurate
17 This formula is often used in science. v=u+at Work out the value of a when v=5.2, u=1.4 and 1=72. Round your answer to an appropriate degree of accuracy.
16 A football club sells, on average, 23 000 tickets per match.In one season they play, on average, 46 matches.How many tickets do they sell, on average, each season?Round your answer to an appropriate degree of accuracy.
15 Gerry's electric toothbrush rotates the brush 125 times per second.Gerry brushes her teeth for two minutes, twice a day.How many rotations does her electric toothbrush make in one week?Give your answer correct to one significant figure (1 s.f.).
14 The instructions on a packet of rice say you should cook 75 g per person.Yuang carefully weighed out 75g of rice.He counted the grains and found he had 2896 grains of rice.Work out the average (mean) mass of a single grain of rice.Give your answer correct to three significant figures (3 s.f.).
13 Round the number 530.403977 to the stated number of significant figures (s.f.).1 s.f.b 2 s.f.3 s.f.a c4 s.f.5 s.f.6 s.f.d fe
12 Gina drove from her house in Madrid to a friend's house in Paris, a distance of 1275.3 km.Gina then drove to another friend's house in Rome, a distance of 1445.2 km.How far did Gina drive altogether?Give your answer correct to two significant figures (2 s.f.).
11 a Use a calculator to work out the answer to 24.2ªxv83/ 7 Write all the numbers on your calculator display.b Round your answer to part a to the stated number of significant figures (s.f.).1 s.f.ii iii 3 s.f.2 s.f.5 s.f.iv 4 s.f.vi 6 s.f.V
10 Which is the correct answer in each case, A, B, C or D?567 rounded to 1 s.f.a 500 A 5 B6 CD 600 b15.493 rounded to 2 s.f.A 15 B16 C15.49 D15.50 c0.07887 rounded to 3 s.f.A 0.078 B0.079 C0.0789 D0.0790 d0.00777777 rounded to 4 s.f.A 0.0077 B0.0078 C0.007777 D0.007778 0.03963 rounded to 2 s.f.℮A
9 Round each number to the given number of significant figures (s.f.).2468.15 (1 s.f.)759.233 (2 s.f.)5.3691 (3 s.f.)b ac 0.0781 (1 s.f.)0.1954 (2 s.f.)d f6.038 88 (3 s.f.)℮964 (1 s.f.)h 0.899 (2 s.f.)19.985 (3 s.f.)1 g
8 This is part of Li's homework.Question Round each number to 3 s.f.b 0.002 058 84 a 2374 650 Answer a 237 b 0.002 Li has rounded one large number and one small number to three significant figures. Both answers are wrong. a Explain the mistakes Li has made. b Write the correct answers.
7 Round each number to two significant figures (2 s.f.). All the answers are in the circle. a 358 b 0.361 d 0.003 5601 e 35.99 C 3572 f 3.6009
6 Round each number to one significant figure (1 s.f.). Choose the correct answer: A, B or C. a 468 A 5 B 50 C 500 b 9.02 A 10 B 9 C 0.9 5686 A 6000 B 5000 C 6 d 0.0035 A 4 B 0.04 C 0.004
5 Round each number to 2 significant figures.0.005671 0.000 038 1 d0.688 0.0231 ba C
4 Use Paolo's method to round each number to I significant Paolo's method to figure. Use 0.005671 0.000 038 1 0.0231 db 0.688 ac
3 Round each number to 3 significant figures. 3 a 4729 b 66549 2355244 Paolo uses this method to round 0.002432 to 1 significant figure.Draw a line after the first s.f. and circle the next digit. The circled digit is a 4, so leave the 2 as it is. Do not write the 4, 3 or 2 but remember to write all
2 Round each number to 2 significant figures.213 4823 185 255 b23 850 da C
1 Use Erin's method to round each number to 1 significant figure.4823 23 850 185255 213 bd ac
16 This is part of Ceri's homework.Question'When you multiply a number with one decimal place by 0.01 you will always get an answer smaller than zero.'Write one example to show this statement is not true.Answer 345.8×0.01 = 3.458 and 3.458 is not smaller than zero so the statement is not true.For
15 Alicia thinks of a number.Alicia divides her number by 0.01, and then multiplies the answer by 0.1.Alicia then divides this answer by 0.01 and gets a final answer of 2340.What number does Alicia think of first?Explain how you worked out your answer.
14 The diagram shows a triangle of height 0.1 m.The area of the triangle is 1.16m2.The formula for the area of a triangle is A= - bh Rearrange the formula to make b the subject. 0.1 m base
13 A tiler works out the area of the wall he is going to tile.The tiler uses this formula to work out the extra area of tiles he must order due to wastage.E=0.14 where:E is the extra area 4 is the area of the wall The diagram shows the dimensions of the wall he is going to tile.a Work out the extra
12 Which calculation, A, B, C or D, gives a different answer to the other three?Show your working.B 96×0.01 C 9.6×0.1 D 96=0.01 A 0.096=0.1

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