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s DECIMALSDECIMALSDECIMALS
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Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
1
How does it work? Solutions Decimals
Page 3 questions
Page 4 questions
Place value of decimals
Place value of decimals
b ca
e fd
b ca
e fd
b ca
e fd
b ca
e fd
8 . 1 7 1 6 1 5 4 . 3 2 1 2 3 0
9 . 1 2 4 2 1 1 6 . 1 2 3 2 1 0
2
3
4
1 0.02
0.003
0.9
0.000 06
0.0001
0.000 008
103
10 0009
10051
10 00011
10007
1001
5 hundredths
or1005
201=
6 ten thousandths
or10 000
650003=
0 ten thousandths
or10 000
00 =
3 tenths
or103
1 thousandths
or10001
4 hundredths
or1004
251=
1 0 0 . 1 0 0 1 0 0 1
3 . 1 2 0 6 1 9
a
b
c
d
e
f
.
.
40.2685 4 10 2 6 8 5
.
.
.
4 19 4 1 1101 9
1001
29 281 2 10 9 1 2101 8
1001 1
10001
101
1001
10001
10 0001
3 74932 3 1 7101 4
1001 9
10001 3
10 0001 2
100 0001
0 2306 2101 3
1001 6
10 0001
0 0085 810001 5
10 0001
# # #
# # # # #
# # # # #
# # # # # #
# # #
# #
= + +
= + + + +
= + + + +
= + + + + +
= + +
= +
5
Decimals Solutions
Mathletics Passport © 3P Learning
2 6HSERIES TOPIC
How does it work? Solutions Decimals
Page 4 questions
Page 6 questions
Place value of decimals
Approximations through rounding numbers
a
a
b
b
c
c
6
1
2
(i)
(i)
(i)
(i)
(i)
(i)
(ii)
(ii)
(ii)
(ii)
(ii)
(ii)
(iii)
(iii)
(iii)
(iii)
(iii)
(iii)
536 . 540
0.73 . 0.7
14 302 . 14 300
2.41 . 2.41
98 542 . 99 000
10.476 . 10.476
8514 . 8510
3.45 . 3.5
4764 . 4800
0.01 . 0.01
18 401 . 18 000
0.386 . 0.386
93 025 . 93 030
11.9 . 11.9
80 048 . 80 000
1.00 . 1.00
120 510 . 121 000
0.049 . 0.049
.
.
.
.
2 0 3 0.203
.
.
1 1 4101 6
1001 1 46
4 10 9 1 0101 7
1001 49 07
5 100 2 10 0 1 2101 1
1001 8
10001 520 218
6 1 8101 5
1001 0
10001 2
100001 9
1000001 6 850 29
101
1001
10001
61001 7
10001 0
10 0001 1
1000001 0 067 01
3101 4
1001 1
10001 0
100001 8
1000001 0 34108
# # #
# # # #
# # # # # #
# # # # # #
# # #
# # #
# # # # #
#
+ + =
+ + + =
+ + + + + =
+ + + + + =
+ + =
+ + + =
+ + + + =
e
a
b
c
d
f
g
[nearest ten] [nearest hundred] [nearest thousand]
[nearest tenth] [nearest hundredth] [nearest thousandth]
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
3
How does it work? Solutions Decimals
Page 6 questions
Approximations through rounding numbers
a
c
3 (i)
(i)
(ii)
(ii)
(iii)
8.8 m
3459 km
10 m
b (i)
(ii)
0.0002 m
0.00 m
3500 km
These digits combine to represent 532 m. This is really small part of the total distance of approximately 3500 km (0.15% of the total distance). So they are not really important as they do not have any effect on the approximate distance between the cities. Only important if a great deal of accuracy was needed.
Page 7 questions
Approximations through rounding numbers
b ca
e
h
f
i
d
g
4
1.98 . 2.0 398 . 400 11.899 . 11.90
79.9 . 80 0.1398 . 0.140 2.1995 . 2.200
49 798 . 50 000 199.9 . 200 9.89 999 . 9.9000
[one decimal place]
[nearest ones]
[nearest thousand]
[nearest ten]
[three decimal places]
[nearest ones]
[two decimal places]
[three decimal places]
[four decimal places]
a b(i) (i)
(ii) (ii)
(iii) (iii)
2500 9600 L
2 9599.59 L
2496 No. Because any digit in this place value (ten thousandths) will not have any affect on the approximate number of litres leaked from the pool.
5
Decimals Solutions
Mathletics Passport © 3P Learning
4 6HSERIES TOPIC
How does it work? Solutions Decimals
Page 9 questions
Decimals on the number line
1
2
3
0.0 1.0
0.1 0.2
2.3 2.4
a
c
e
0.7
0.13
2.34
2.0 3.0
9.1 9.2
5.21 5.22
b
d
f
2.1
9.15
5.212
a
c
e
1.6
0.94
2.053
b
d
f
4.2
7.07
9.538
1.0 2.0 4.0 5.0
0.9 1.0 7.0 7.1
2.05 2.06 9.53 9.54
` the value . 0.3
` the value . 0.8
` the value . 1.995
` the value . 2.902
` the value . 1.03
` the value . 0.09
` the value . 8.104
` the value . 0.990
0.2 0.3
0.8 0.9
1.994 1.995
2.902 2.903
a
c
e
g
[tenth]
[tenth]
[thousandth]
[thousandth]
[hundredth]
[hundredth]
[thousandth]
[thousandth]
1.03 1.04
0.08 0.09
8.103 8.104
0.989 0.990
b
d
f
h
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
5
How does it work? Solutions Decimals
Page 11 questions
Multiplying and dividing by powers of ten
b
c
a
e f
d
1
8.0 0 . = 800
2
12 . 4 5 0 0 . = 124 500
4
3.4 . = 34
1
0 . 5 1 . 2 =51.2
2
29. 0 0 0 . = 29 000
3
0 . 0 0 0 0 4 6 . 9 = 46.9
6
b
b
c
c
a
a
e
e
f
f
d
d
2
3
0 . 0 2 . =0.02
2
3 1 . 0 0. = 3100
2
0 . 0 0 7 0 . 8 0 = 0.00708
4
9 0 . 0 0 8 0 . = 90 0080
4
4 . 5 9 0 . = 4.59
3
0 . 0 2 4 0 0 . = 0.02 400
5
1 . 3 6 7 . 5 1 2 = 1.367512
3
0 . 0 0 3 . 4 5 = 0.003 45
3
0 . 0 . 0 1 4 = 0.0014
1
0 . 0 0 2 7 0 0 . = 2700
6
0 . 0 0 4 2 1 9 0 0 . = 0.004 219
8
0 . 2 1 5 9 9 5 1 . = 0.215 995 1
7
8 100#
29 1000#
3.4 10#
12.45 10000#
0.512 100# 0.0000469 1000000#
1002 ' 4590 1000'
.0 014 10' 70. 0 100008 '
.1367 512 1000' 421900 100000000'
31 102# 2400 105
'
0.0027 106# 90.008 104
#
.3 45 103' 2159 951 107
'
Decimals Solutions
Mathletics Passport © 3P Learning
6 6HSERIES TOPIC
How does it work? Solutions Decimals
Page 12 questions
Page 14 questions
Multiplying and dividing by powers of ten
Terminating decimals to fractions
4
1 b c da
g
j
h
i k l
e f
0 and 9 8 and 9 8 and 7 9 and 2 0 and 7
IR A D X P O I N T
a
b
c
d
e
f
g
h
i
j
(i) I
N
A
O
X
T
R
I
D
P
2 8 3 0 3 9 2 0
2 3 8 5 7
0 4 7 6 3 8 9 2
3 8 2 9 6 2
1 9 2 3 8 0 7
8 9 2 3 6 7 0 1
2 0 9 1 7 9 8 3
0 8 3 9 1 7
9 0 2 8 7 3 2 0 1
0 0 8 3 9 0
3 and 8
8 and 9
8 and 2
0 and 7
6 and 7
0 and 9
0 and 8
8 and 7
3 and 9
9 and 2
3 and 9 8 and 2 0 and 8 3 and 8 6 and 7
.0 1101=
.0 00110001=
.0 1291000129=
.0 031003=
.0 049100049=
0.060110 000601=
0.7107=
.0 00710007=
.0 081100081=
.0 091009=
.0 013100013=
0.100710 0001007=
2830.3920 100#
23857 1000'
0.4763892 105#
382 961 10000'
19238.07 101#
8.9236701 10000#
20 917 9831000000
1#
83917 105'
902873.02110
12
#
0.08390 103#
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
7
How does it work? Solutions Decimals
Page 14 questions
Page 15 questions
Terminating decimals to fractions
Terminating decimals to fractions
b
b
b
e
h
c
c
c
f
i
a
a
a
d
g
e
e
h
k
f
f
i
l
d
d
g
j
2
3
4
0.5105
21= =
. 22 3103=
2.8 2108
254
=
=
3.05 31005
3201
=
=
1.004 110004
12501
=
=
1.4 1104
152
=
=
2.75 210075
243
=
=
2.025 2100025
2401
=
=
4.06 41006
4503
=
=
5.005 510005
52001
=
=
3.144 31000144
312518
=
=
.0 081008
252= =
. 11 031003=
.0 1210012
253= =
.0 045100045
2009= =
.0 2510025
41= =
.0 002810 00028
25007= =
.0 022100022
50011= =
.0 060510 000605
2000121= =
.0 00410004
2501= =
. 44 00110001=
.0 00510005
2001= =
. 22 00910009=
.0 6106
53= =
1. 11101=
.0 021002
501= =
. 33 071007=
Decimals Solutions
Mathletics Passport © 3P Learning
8 6HSERIES TOPIC
How does it work? Solutions Decimals
Page 17 questions
Page 18 questions
Fractions to terminating decimals
Fractions to terminating decimals
b
b
e
h
c
c
f
i
a
a
e
i
b
b
f
j
c
c
g
k
d
d
h
a
a
d
g
1
2
3
4
.
51
102
0 2
=
=
2012
.
22
106
0 6`
'' =
=
100
.
254 16
0 16
=
=
2 2
.
259
10036
2 36
=
=
.
41
10025
0 25
=
=
54
.
22
2520
54
108
0 8
55
`
''
#
#
=
=
= .
2418
43
43
10075
0 75
66
2525
#
#
`
'' =
=
=
.
2001
10005
0 005
=
=
1 1
.
2001
10005
1 005
=
=
.
2511
10044
0 44
=
=
.
1256
100048
0 048
=
=
8 8
.
507
10014
8 14
=
=
21
105=
258
10032=
1154
108=
52
104=
2503
100012=
33251
1004=
43
10075=
20011
100055=
209
10045=
1252
100016=
66207
10035=
.109 0 9= .
1003 0 03= .
10011 0 11= .
10007 0 007=
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
9
How does it work? Solutions Decimals
Page 18 questions
Page 19 questions
Fractions to terminating decimals
Fractions to terminating decimals
e
b
h
e
f
c
f
d
a
g
d
4
5
4022
2011
.
22
55
2011
10055
0 55
#
#
`
'' =
=
=
.
.
.
.
52 2 000 5
5 2 0 0 0
0 4 0
0 4
2
'=
=
=
g
160036 1
.
66
1006
1 06`
'' =
=
.
8 . 0 0 0
.
.
58 8 000 5
5
1 6 0
1 6
3
'=
=
=
g
759
253
.
33
44
253
10012
0 12
#
#
`
'' =
=
=
.
.
.
.
41 1 000 4
4 1 0 0 0
0 2 5
0 25
1 2
'=
=
=
g
215012 2
2504 2
.
33
22
504
1008
2 08
#
#
`
'' =
=
=
.
1 . 0 0 0
.
.
811 11 000 8
8 1
0 1 3 7 5
1 375
1 3 6 4
'=
=
=
g
3 12 4 3
.
40 4 103
3 3
''
`
=
=
.
. 0 0 0
.
.
83 3 000 8
8 3
0 3 7 5
0 375
3 46
'=
=
=
g
.
.
.
.
427 27 000 4
4 2 7 0 0 0
0 6 7 50
6 75
2 3 2
'=
=
=
g
Decimals Solutions
Mathletics Passport © 3P Learning
10 6HSERIES TOPIC
How does it work? Solutions Decimals
Page 20 questions
Fractions to terminating decimals
b
e
c
f
a
d
6
.
.
.
.
1512
54
4 000 5
5 4 0 0 0
0 8 0
0 8
33
4
` '
'' =
=
=
=
g
818
9.000 4
4 9 . 0 0 0
.
.
22
49
2 2 50
2 25
1 2
` '
'' =
=
=
=
g
9 3
3.000 4
4 3 .
.
.
12 3 43
0 0 0
0 7 5 0
0 75
3 2
''
` '
=
=
=
=
g
2481
27.000 8
8 2 7 . 0 0 0
.
.
33
827
0 3 3 7 5
3 375
2 3 6 4
` '
'' =
=
=
=
g
5649
7.000 8
8 7 . 0 0 0
.
.
77
87
0 8 7 5
0 875
67 4
` '
'' =
=
=
=
g
1626
13.000 8
8 1 3 . 0 0 0
.
.
22
813
0 1 6 2 5
1 625
1 5 2 4
` '
'' =
=
=
=
g
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
11
Where does it work? Solutions Decimals
Page 22 questions
Page 23 questions
Adding and subtracting decimals
Adding and subtracting decimals
1
2
3
c da b
g he
a
d
a
f
0 . 1 4 +
0 . 7 3
0 . 8 7
0 . 9 9 -
0 . 2 6
8 . 7 5 +
1 . 2 4
2 . 1 9 +
5 . 6
0 . 1 3
0 . 7 3
9 . 9 9
7 . 9 2
1 . 6 8 +
5 . 3 0
6 . 9 8
0 . 2 4 6 +
0 . 8 3 2
1 . 0 7 8
5 . 12 4 -
01 . 8 3
4 . 4 1
5 . 10 7 4 -
11 . 0 6 4
4 . 0 1
1 2 . 1 9 4 +
9 . 0 5 7
2 1 . 2 5 1
2 4 . 11 15 8 -
1 31 . 61 9 4
1 0 . 4 6 4
11.3 - 0.2 . 11 - 0
. 11
5.7 + 6.2 . 6 + 6
. 12
8.3 - 1.9 . 8 - 2
. 6
(i)
(iii)
8.34 + 1.61 + 0.54 . 8 + 2 + 1
. 11
2.71 + 3.80 + 1.92 . 3 + 4 + 2
. 9
(v) (vi)
(iv)
(ii) 0.9 + 9.4 . 1 + 9
. 10
Add 8.75 to 1.24
Add 2.19, 5.6 and 0.13 e
b
4 . 7 9 -
3 . 1 5
1 . 6 4
8 . 16 10 11 12 -
01 . 91 31 51 6
7 . 6 6 5 6
Subtract 3.15 from 4.79
Subtract 0.9356 from 8.6012
c
d
0 . 9 3 6 +
0 . 8 6 5
1 . 8 0 1
1 0 . 2 0 6 +
4 . 6 4
8 . 0 1 5 9
2 2 . 8 6 1 9
Add 10.206, 4.64 and 8.0159
Add 0.936 to 0.865
Decimals Solutions
Mathletics Passport © 3P Learning
12 6HSERIES TOPIC
Where does it work? Solutions Decimals
b
a b
c
a b c
2 . 7 1 +
3 . 8 0
1 . 9 2
8 . 4 3
8 . 3 4 +
1 . 6 1
0 . 5 4
1 0 . 4 9
7 . 8 10 -
2 . 51 6
5 . 2 4
1 13 . 10 9 10 10 -
1 81 . 4 61 21 1
5 . 5 12 10 10 10 -
0 . 11 21 51 31 2
Page 23 questions
Page 25 questions
Adding and subtracting decimals
Multiplying with decimals
3
4
1
(v) (vi)
.10 49 10. .8 43 8.
4 . 6 2 7 9
0 . 3 9 4 6 8
. . .7 8 2 56 5 24` - = . . .13 09 8 4621 4 6279` - =
. . .0 52 0 12532 0 394 68` - =
.0 8 2#
8 2 16# =
.5 1 5#
5 15 75# =
.0 14 6#
14 6 84# =
1 d.p. in question` 1 d.p. in answer
1 d.p. in question` 1 d.p. in answer
2 d.p. in question` 2 d.p. in answer
0.8 2 1.6#` = 5 1.5 7.5#` = 0.14 .6 0 84#` =
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
13
Where does it work? Solutions Decimals
d
a
e
b
f
c
d e f
Page 25 questions
Multiplying with decimals
1
2
.0 62 4#
62 4 248# =
2 d.p. in question` 2 d.p. in answer
0.62 .4 2 48#` =
. .3 8 0 2#
38 2 76# =
2 d.p. in question` 2 d.p. in answer
3.8 . .0 2 0 76#` =
.3 0 032#
3 32 96# =
3 d.p. in question` 3 d.p. in answer
3 . .0 032 0 096#` =
1.09 .0 08#
4 d.p. in question` 4 d.p. in answer
1.09 . .0 08 0 0872#` =
.1 134 2#
1134 2 2268# =
3 d.p. in question` 3 d.p. in answer
1.124 .2 2 268#` =
2.7 .2 5#
7.1 .1 4# 3.21 .2 1# 17.2 .9 3#
2 d.p. in question` 2 d.p. in answer
2 d.p. in question` 2 d.p. in answer
3 d.p. in question` 3 d.p. in answer
2 d.p. in question` 2 d.p. in answer
2.7 . .2 5 6 75#` =
7.1 . .1 4 9 94#` = 3.21 . .2 1 6 741#` = 17.2 . .9 3 159 96#` =
109 #
872
78
27 #
135
540
675
25
7 1 #
284
710
994
14
321 #
321
6420
674 1
21
172 #
516
15480
15996
93
Decimals Solutions
Mathletics Passport © 3P Learning
14 6HSERIES TOPIC
Where does it work? Solutions Decimals
Page 27 questions
Dividing with decimals
1
2
a
a
b
b
c
c
3.6 4' 17.5 5' .16 2 9'
d
d
e
e
f
f
0.63 3' .0 489 5' .10 976 7'
3.6 4 .0 9` ' = 17.5 5 .3 5` ' = 16.2 9 .1 8` ' =
0.63 3 .0 21` ' = 0.489 5 .0 0978` ' = 10.976 7 .1 568` ' =
4 .
.
3 6 0
0 9 03
= g
.
.3 0 6 3
0 2 1= g
7 . 5
.
5 1
0 3 51 2
= g
5 . 4 8 9 0
.
0
0 0 9 7 84 3 4
= g
.
.
.
. .
52 0 4
4 5 2 0
1 3 0
5 2 0 4 13
1
'
` '
=
=
g
.
.
.
. . .
15 8 4
4 1 5 8 0
0 3 9 5
1 58 0 4 3 95
1 3 2
'
` '
=
=
g
.
.
.
. .
96 0 6
6 9 6 0
1 6 0
9 6 0 6 16
3
'
` '
=
=
g
.
.
.
. . .
81 25 5
5 8 1 2 5
1 6 2 5
0 8125 0 05 16 25
3 1 2
'
` '
=
=
g
.
.
.
. . .
5 6 8
8 5 6
0 7
0 56 0 8 0 7
5
'
` '
=
=
g
.
.
.
. . .
5368 2 6
6 5 3 6 8 2
0 8 9 4 7
5 3682 0 006 894 7
5 5 2 4
'
` '
=
=
g
6 . 2
.
9 1
0 1 87
= g
0 . 9 7 6 0
.
7 1
0 1 5 6 83 4 5
= g
. .45 2 0' . .9 6 0 6' . .0 56 0 8'
. .1 58 0 4' 0. .8125 0 05' . .5 3682 0 006'
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
15
Where does it work? Solutions Decimals
c z h m n a f b
.0 14o .0 4r .41 1o .0 144 0.141o o .0 41o .414 .0 401o o .4 1o .0 41o o
4.1414 ... C z F h N d W c D b A a U n P t L f O m
0.144144 ... Y n A m R f T t K z E h R d I c U b S a
0.1444 ... L a D b A m I h M t B f S c A d U z Q n
0.401401 ... R h Z d A n E z A c N t 0 a M b A h G f
4.111 ... A f T z P c H d T a Y n A t A h C m A b
0.4111... I d Y t A b U n H m I z E f S m I t T a
0.4141 ... A b L a D t E f A d N c L m E z O d N h
41.111 ... W c J f B d A a X h M m A b U n A A z
0.444 ... P m V c E a F b A n B d T Y f E c I t
0.1411411 ... H t A n A m A m U f A b A h A a D d R c
Page 29 questions
Recurring decimals
1
V I N C U L U M
2 a b c
d e f
.
.
.
3 1 0 0 0
0 3 3 3
1 3 0 3
1 1 1
` ' = o
g
.
.
. .
6 1 6 0 0
0 2 6 6
1 6 6 0 26
1 4 4
` ' = o
g .
.
. .
9 2 5 0 0
0 2 7 7
2 5 9 0 27
2 7 7
` ' = o
g .
.
. .
3 0 3 4 0 0
0 1 1 3 3
0 34 3 0 113
1 1
` ' = o
g
.
.
.
9 4 0 0 0
0 4 4 4
4 9 0 4
4 4 4
` ' = o
g .
.
.
6 5 0 0 0
0 8 3 3
5 9 0 83
5 2 2
` ' = o
g
1 3' 4 9' 5 6'
1.6 6' .2 5 9' .0 34 3'
Decimals Solutions
Mathletics Passport © 3P Learning
16 6HSERIES TOPIC
Where does it work? Solutions Decimals
Page 30 questions
Recurring decimals
3
.
. ...
.
3 2 0 0 0 0 0
0 6 6 6 6 6
2 3 0 6
2 2 2 2 2
` '
=
= o
g
.
. ...
. .
7 1 6 0 0 0 0
0 2 2 8 5 7
1 6 7 0 228 57
1 2 6 4 5
` '
=
=
g
6 . 8 0 0 0 0
. ...
. . .
3
2 2 6 6 6 6
0 68 0 3 2 26
2 2 2 2
` '
=
= o
g
.
. ...
. .
3 2 9 0 0 0 0
0 9 6 6 6 6
2 9 3 0 96
2 2 2 2 2
` '
=
= o
g
.
. ...
. . .
6 1 9 0 0 0 0
0 3 1 6 6 6
0 019 0 06 0 316
1 1 4 4 4
` '
=
= o
g
.
. ...
. . .
8 3 3 0 0 0 0
0 4 1 2 5 0
0 33 0 8 0 4125
3 1 2 4 2
` '
=
=
g
.
. ...
.
6 1 0 0 0 0 0
0 1 6 6 6 6
1 6 0 16
1 4 4 4 4
` '
=
= o
g .
. ...
. ...
7 1 0 0 0 0 0
0 1 4 2 8 5
1 7 0 142 85
1 3 2 6 4
` '
=
=
g
a b c2 3' 1 6' 1 7'
d e f.1 6 7' .2 9 3' . .0 33 0 8'
g h i0.6 .38 0' 0. .019 0 06' 0. 0.00644 002'
Recurring decimal?Yes No
X Recurring decimal?Yes No
X Recurring decimal?Yes No
X
Recurring decimal?Yes No
X Recurring decimal?Yes No
X Recurring decimal?Yes No
X
Recurring decimal?Yes No
X Recurring decimal?Yes No
X Recurring decimal?Yes No
X
.3 3 8'=
.8 36 '= .1 9 6'= .6 44 2'=
.
.
. . .
2 6 4 4 0 0 03 2 2 0 0 0
0 00644 0 002 3 22` '
=
=
g
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
17
What else can you do? Solutions Decimals
Page 32 questions
Page 34 questions
Simple recurring decimals into single fraction
Combining decimal techniques to solve problems
2
1
3
a
a
d
g
b
e
h
c
f
i
195
396 3
32=
999162
376=
59912 5
334=
599991485 5
10115=
999117
11113=
99994896
1111544=
297 4
93 4
31=
(i)
(ii)
.0 999 1= =o
0.9 0.999999... 1.= =o Even though the value appears as 0.9 repeater, it actually equals a whole number
Amount of yellow paint mL0.5 12.46#=
3 d.p. in question` 3 d.p. in answer
1246 #
6230
1 2 3 5
mL0.5 12.46 6.23#` = of yellow paint
1 a
d
b
e
c
f
94
9911
91=
98
9927
113=
96
32=
9957
3319=
Decimals Solutions
Mathletics Passport © 3P Learning
18 6HSERIES TOPIC
What else can you do? Solutions Decimals
Page 34 questions
Combining decimal techniques to solve problems
1
2
3
b
a
b
c
Amount of yellow paint mL0.5 1 .8 45#=
3 d.p. in question` 3 d.p. in answer
1845 #
9225
4 2 2 5
mL0.5 . .18 45 9 225#` = of yellow paint
` Amount of dark-green paint mL
mL (nearest tenth)
18.45 9.225 27.675
27.7
= + =
=
2 d.p. in question` 2 d.p. in answer
9345 #
46725
1 2 2 5
` Number of words typed in 5 minutes = 467.25
. 467 words
5 skaters had times less than 126.245 seconds...so 5 skaters made it into the team.
Slowest time recorded = 126.268 seconds
. . .126 245 0 01 126 255+ =
So 2 skaters missed out by less than 0.01 seconds
Decimals Solutions
Mathletics Passport © 3P Learning
6HSERIES TOPIC
19
What else can you do? Solutions Decimals
Combining decimal techniques to solve problems
Page 35 questions
4
5
The minimum signal for 3 bars is 0.61, therefore need to calculate 0.61 ' 0.04
The total time for spaces between songs = 0.15 # 4
15 #
4
60
2 d.p. in question` 2 d.p. in answer
` The total time for spaces between songs = 0.60 min
` 0.15 # 4 = 0.60
The total length of the video min
min
minutes to the nearestminute
. . . . . .
.
3 55 5 14 2 27 3 18 4 86 0 60
19 6
20
`
.
= + + + + +
=
If Laura is working 16.25 m away from the antenna, then the signal drops a total of 16.25 # 0.024
16250
24
65000
325000
390000
#
Since 5 decimal places in question, need 5 decimal places in answer
3 9 0 0 0 0
5 4 3 2 1
` 3.9 signal strength drop when 16.25 m away
` 1.0 - 3.9 signal strength = 0.61 signal strength
` Laura will have 3 bars of signal strength (but only just!)
Decimals Solutions
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20 6HSERIES TOPIC
What else can you do? Solutions Decimals
Page 36 questions
7
8
The total amount of "Sal-X" 863.999... 138.222...
. ...725 777
= -
=
The amount of "Sal-X" in each jar = 725.777... ' 4
7 2 5 . 7 7 7
. ...
4
1 8 1 4 4 43 1 1 1g
` The amount of "Sal-X" in each jar mL
mL to the nearest whole mL
.181 4
181.
= o
Every .0 3o hours = every 31 of an hour = 3 times an hour!
3 # 0.2 = 0.6
` The waves increase in height by 0.6 m every hour.
` The time taken to get to a surf-able height 14 0.6
14 6
'
'
=
=
hours.2 3= o
1 4 . 0 0 0
. ...
6
0 2 3 3 31 2 2 2g
hours minutes
hours minutes
1.0 60
0.3 20`
=
=o
` people start surfing after 2 hours, 20 minutes.
6 The total number of people was not a perfect multiple of the number of houses surveyed, which will give a decimal answer...so, on average there are 3.4 people in each house, but each house will have different numbers, leading to this result.
Combining decimal techniques to solve problems
4
DECIMA
LS ON
THE NUMBER LINE DECIMALS ON THE NUM
BE
R LINE
..../.....
/20...
MU
LTIPLYING AND DIVIDING BY POWERS
OF TEN
..../...../20.
..
MULTIPLY
ING WITH DECIMALS MULTIPLYING WITH DE
CIMALS
..../.....
/20...
DIVIDING WITH DECIMALS DIVIDING
WITH DECIMAL
S
..../...../20...÷
PLACE
VALUE OF DECIMALS PLACE VALUE O
F DECIMALS
..../...../20...
