Maths

Number
1
Activity 8
1. (a) 50% ( b) 25% (c) 60% (d) 48% (e) 160%
(f ) 765% (g) 23% ( h) 200% (i) 70% ( j) 18%
2. (a) 0⋅2 = 1__ 8
5
( b) 0⋅32 = ___ 67
25
(c) 0⋅67 = ____
100
(d) 0⋅18 = ___ 9
50
(e) 0· 6 ˙ = 2__ 1
3
(f) 0⋅04 = ___
25
_____ 23
( g) 0⋅023 =
11
1000
(h) 0⋅11 = ____
100
3. (a) 25%
(b) 33 1_ 3 % (c) 37 1_ 2
% (d) 130% (e) 200% (f ) 25%
(g) 400% ( h) 80% (i) 66 2_ 5
3
% ( j) 10 __
12 %
4. (a) 1__
3 = 0· 3 ˙ = 33 1_ 1__
3
% ( b)
4
= 0·25 = 25%
(c) 1__
6 = 0·1 6 ˙ = 16 2_ 1__
3
% (d)
4
= 0·25 = 25%
(e) 5__
9 = 0· ˙ 5 = 55 5_ 9 %
Activity 9
1. (a) 1 × 10 12 ( b) 2⋅222 × 10 –25 kg (c) 3 × 10 8 m/s
(d) 1⋅4 × 10 9 (e) 6 × 10 24 kg (f ) 1 × 10 18
(g) 1 × 10 21 Bytes ( h) 6⋅2 × 10 –34 Js (i) 1⋅57 × 10 7 K
( j) 5⋅6 × 10 –15 m 2. (a) 2⋅3 × 10 –2 ( b) 1 × 10 3
(c) 1⋅4 × 10 –4 (d) 2 × 10 0 (e) 2⋅43 × 10 –5
(f ) 1·26 × 10 7 (g) 1⋅2 × 10 –5 ( h) 1⋅4 × 10 1
(i) 2⋅67 × 10 2 ( j) 5⋅7 × 10 –9 3. (a) 0⋅03
( b) 0⋅000412 (c) 357 000 (d) 2 000 000
(e) 0⋅00000056 (f ) 0⋅00006 (g) 0⋅0001 ( h) 100 000
(i) 3⋅3 ( j) 780 000 000 4. (a) 6 × 10 5 ( b) 1⋅26 × 10 3
(c) 5⋅6 × 10 9 (d ) 9⋅6 × 10 4 (e) 9 × 10 16 (f ) 5⋅4 × 10 –9
(g) 2 × 10 4 ( h) 5 × 10 7 (i) 2 × 10 1 ( j) 3⋅2 × 10 –2
Activity 10
1. (a) 2⋅3 × 10 0 , 0 ( b) 3⋅5642 × 10 4 , 4
(c) 1⋅3 × 10 –4 , –4 (d) 4⋅765314 × 10 6 , 6
(e) 5⋅63 × 10 –5 , –4 (f ) 7⋅3 × 10 6 , 7 (g) 5⋅6 × 10 –4 , –3
( h) 5⋅12 × 10 –8 , –7 (i) 1⋅0 × 10 5 , 5 ( j) 6⋅4 × 10 –9 , –8
2. (a) 10, 1 ( b) 1000, 3 (c) 0⋅01, –2 (d) 10 000, 4
(e) 10, 1
Activity 11
Accumulated
Percentage error
absolute error
1. l + d = 82 cm 0·2 cm 0·2%
l – d = 12·6 cm 0·2 cm 1·6%
2. m 1
+ m 2
= 59 g 10 g 17%
m 1
– m 2
= 5 g 10 g 200%
3. T 1
+ T 2
= 42·9 °C 0·4 °C 1%
T 1
– T 2
= 12·3 °C 0⋅4 °C 3%
4. (i) d + l = (9⋅5 ± 0⋅2) cm (ii) d – l = (1⋅1 ± 0⋅2) cm
5. d = 4⋅9 mm
Absolute error = ±0⋅2 mm Percentage error = ±4%
d = (4⋅9 ± 4%) mm
Activity 12
1. (a) 9⋅87 (b) 0⋅1 (c) 1⋅9 (d) 4⋅785 (e) 0⋅2639
2. (a) 43⋅0 cm 2 ( b) u = 50⋅24 (c) f = 174
(d) y = 3⋅012 (e) A = 459⋅7
3. (a) 4⋅794 × 10 5 = 479 400 (b) 1⋅33 × 10 0 = 1⋅33
(c) 5⋅732 × 10 1 = 57⋅32 (d) 6⋅0 × 10 0 = 6⋅0
(e) 5⋅73 × 10 –4 = 0·000573 (f) 5⋅2 × 10 –12
(g) 6⋅0 × 10 4 = 60 000 (h) 5⋅63 × 10 –2 = 0⋅0563
(i) 7⋅8 × 10 3 = 7800 ( j) 8⋅3 × 10 4 = 83 000
4. (a) 40 (b) 450 (c) 1 (d) 25 000 (e) 10 (f ) 500
(g) 540 000 (h) 1 (i) 400 ( j) 1
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