guided practice worksheet questions are targeted at the ......d 0.048 ÷ 0.6 e 1.28 ÷ 0.004 f 0.805...
TRANSCRIPT
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�2 3.1 Conversion between fractions and decimals
77A
1 Write each of the following sets of numbers in order of size.
Start with the smallest number each time.
a 0.45, 0.6, 0.5, 0.4, 0.54 b 0.74, 0.4, 0.47, 0.7, 0.44
.............................................................................................. ..............................................................................................
c 0.8, 0.18, 0.88, 0.81, 0.08, 0.1 d 5.63, 5.6, 5.3, 5.06, 5.36
.............................................................................................. ..............................................................................................
e 7.9, 7.039, 7.39, 7.033, 7.93, 7.933
..............................................................................................
2 Write each of these decimals as fractions.
units tenths hundredths thousandths
a 0 . 0 1
b 0 . 0 0 9
c 0 . 5 3
d 4 . 7
e 5 . 0 8 3
3 Write each of these decimals as fractions.
a 0.7 ............................ b 0.09 ............................ c 0.003 ............................ d 0.13 ............................
e 3.1 ............................ f 0.029 ............................
4 Write each of these as fractions in their simplest form.
a 0.8 .................................................................................. b 0.36 ..................................................................................
c 0.006 ............................................................................. d 0.128 ...............................................................................
e 3.75 ............................................................................... f 8.02 ..................................................................................
g 23.025 ........................................................................... h 7.0056 .............................................................................
Guided practice worksheet
Write the numbers underneath each other, in the space below, with the decimal points lined up.
a ........................................................................
b ........................................................................
c ........................................................................
d ........................................................................
e ........................................................................
The place value of the last column each time gives you the denominator of the fraction.
Questions are targeted at the grades indicated
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�2 3.1 Conversion between fractions and decimals
77B
Guided practice worksheet
5 Write each of these fractions as a decimal.
a 4
100 .................................................... b 65
100 .................................................... c 7
10 .........................................................
d 2
1000 ................................................... e 343
1000 .................................................. f 3
100000 ....................................................
6 Write each of these fractions as a decimal.
a 35 ....................................................... b
150 .................................................... c
320 ..........................................................
d 625 ...................................................... e
34 ....................................................... f
63250 .........................................................
g 14 ....................................................... h
950 ..................................................... i
12 ...........................................................
j 39
500 .................................................... k 101200 .................................................... l
3125 ........................................................
7 Write the following sets of numbers in order. Start with the smallest each time.
a 45, 0.45, 0.85, 1925, 0.78 b
14, 0.2,
310,
25, 0.35
....................................................................... .......................................................................
c 57100, 35, 0.58, 0.65,
1425 d
920, 0.43,
1125, 0.34, 0.4
....................................................................... .......................................................................
e 1725, 0.7, 35, 0.69,
1320
.......................................................................
To order a mixture of fractions and decimals, � rst change the fractions into decimals.
If the number on the bo� om of a fraction is 10, 100, 1000, etc then this tells you the number of decimal places in the decimal.
If the number on the bo� om of a fraction is not 10, 100, 1000. etc, then turn the fraction into an equivalent fraction with one of these numbers on the bo� om.
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�2 3.2 Carrying out arithmetic using decimals
79A
1 Work out
a 5.46 + 6.39 b 23.1 + 5.43 c 46 + 4.35 + 0.8
............................................ ............................................ ............................................
d 74.35 – 8.62 e 78.9 – 6.37 f 9.83 – 2.347
............................................ ............................................ ............................................
2 Work out
a 34 × 1000 b 57.2 × 10 c 9.03 × 1000
............................................ ............................................ ............................................
d 0.045 × 100 e 0.621 × 1000 f 43.9 × 100
............................................ ............................................ ............................................
3 Work out
a 13 ÷ 10 b 420 ÷ 100 c 8 ÷ 100
............................................ ............................................ ............................................
d 12.6 ÷ 100 e 3.4 ÷ 100 f 23.52 ÷ 10
............................................ ............................................ ............................................
4 Work out
a 0.3 × 0.4 b 0.07 × 0.08 c 0.01 × 0.4
............................................ ............................................ ............................................
Guided practice worksheet
Count the total number of decimal places in the question; the answer must have the same number of decimal places.
Remember to line up the decimal points.
Questions are targeted at the grades indicated
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�2 3.2 Carrying out arithmetic using decimals
79B
Guided practice worksheet
d 0.006 × 0.5 e 1.2 × 0.3 f 4.3 × 0.02
............................................ ............................................ ............................................
5 Work out
a 2.43 × 2.1 b 1.85 × 0.32 c 92.3 × 5.3
............................................ ............................................ ............................................
d 6.75 × 0.43 e 0.123 × 0.45 f 0.048 × 2.7
............................................ ............................................ ............................................
6 Work out
a 16 ÷ 0.2 b 15 ÷ 0.03 c 24 ÷ 0.4
............................................ ............................................ ............................................
d 48.2 ÷ 0.2 e 68.4 ÷ 0.04 f 3.75 ÷ 0.05
............................................ ............................................ ............................................
7 Work out
a 4.2 ÷ 0.3 b 0.145 ÷ 0.5 c 19.2 ÷ 0.03
............................................ ............................................ ............................................
d 0.048 ÷ 0.6 e 1.28 ÷ 0.004 f 0.805 ÷ 0.007
............................................ ............................................ ............................................
Multiply both numbers by a power of 10 so that the second number is no longer a decimal.
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�2 3.3–3.4 Rounding, decimal places and signi� cant � gures
81
1 Write each of these numbers correct to 1 signi� cant � gure.
a 6.4 ...................................... b 3.8 ...................................... c 17.8 ......................................
d 378 ...................................... e 94.79 ......................................
2 Write each of these numbers correct to 1 signi� cant � gure.
a 0.64 ...................................... b 0.0038 ...................................... c 1.0038 ......................................
d 0.0099 ...................................... e 0.6009 ......................................
3 Write each of these numbers correct to 3 signi� cant � gures.
a 6.456 ...................................... b 3.142 ...................................... c 17.88 ......................................
d 37802 ...................................... e 94.01 ......................................
4 Write each of these numbers correct to 3 signi� cant � gures.
a 0.6411 ...................................... b 0.03088 ...................................... c 1.0038 ......................................
d 0.009999 ...................................... e 0.6009 ......................................
Do not forget that that there must be only one � gure in your answer that is not a zero.
Zeros in the middle of a number are signi� cant.
Don’t forget there is a di� erence between 6.0 (2 signi� cant � gures) and 6.00 (3 signi� cant � gures).
Any leading zeros are not signi� cant � gures, so think about the � rst non-zero � gure in each number.
Guided practice worksheet Questions are targeted at the grades indicated
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�2 3.5 Estimating calculations by rounding
83A
1 Work out an estimate in each case by � rst rounding each number correct to 1 signi� cant � gure.
a The area of a rectangle 20.3 cm by 39.2 cm.
.......................................................................................................................................
b The area of a square with a side of length 51 cm.
.......................................................................................................................................
c The total length of 48 rods each of length 5.8 metres.
.......................................................................................................................................
2 Work out an estimate for the value of each of
a 17.8 × 31.1 b 99.8 × 41.2
.............................................................. ..............................................................
c 37.9 × 51.3 d 487 × 316
.............................................................. ..............................................................
3 Work out an estimate for the value of each of
a 49 ÷ 2.1 b 80.5 ÷ 3.9
.............................................................. ..............................................................
c 19.8 ÷ 3.2 d 617 ÷ 4.9
.............................................................. ..............................................................
4 Work out an estimate of the following and state whether your answer is an underestimate or overestimate.
a 499 × 68 b 7.1 × 20.68
.............................................................. ..............................................................
c 18.5 ÷ 4.1 d (21.8 ×11.06) ÷ 4.88
.............................................................. ..............................................................
Guided practice worksheet
Remember that 5.8 m is not 10 correct to 1 signi� cant � gure.
When you round up in the numerator and round down in the denominator, then you make the answer bigger.
D
Questions are targeted at the grades indicated
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�2 3.5 Estimating calculations by rounding
83B
Guided practice worksheet
5 y = p(q + r) p = 17.8, q = 8.9, r = 12.75
Work out an estimate for the value of y.
......................................................................................................................
6 s v ua
=2 2
2− v = 4.8, u = 1.9, a = 21.1
Work out an estimate for the value of s.
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D
C
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�2 3.6 Estimating calculations involving decimals
85A
1 Work out estimates for the values of the following.
a 6.8 × 0.48 ................................................................................... b 0.088 × 0.38 ................................................................................
........................................................................................................ ..........................................................................................................
c 0.75 × 0. 059 ............................................................................. d 0.0028 × 0.0788 .........................................................................
........................................................................................................ ..........................................................................................................
e 0.0682 ...........................................................................................
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2 Work out estimates for the values of the following.
a 5.78 ÷ 0.601 .............................................................................. b 58. 99 ÷ 0.096 .............................................................................
........................................................................................................ ..........................................................................................................
c 199 ÷ 0.51 .................................................................................. d 0.333 ÷ 0. 641 .............................................................................
........................................................................................................ ..........................................................................................................
e 0.028 ÷ 0. 614 ..........................................................................
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3 Work out estimates for the values of the following.
a 19 80 48
..
b 0 680 18..
.................................................................. ..................................................................
c 11 8 5 1
0 48. .
.××
d
0 81 4 890 102
. ..××
.................................................................. ..................................................................
e 0 791 789
0 203.
.×
..................................................................
Guided practice worksheet
When multiplying decimals count the total number of � gures after the decimal point.
When dividing by a decimal multiply both numbers to make the divisor a whole number.
D
C
Questions are targeted at the grades indicated
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�2 3.6 Estimating calculations involving decimals
85B
Guided practice worksheet
4 Work out estimates for the values of the following. In each case state whether your answer is an overestimate or underestimate.
a 7.8 × 0.58 b 39 080 408
..
.................................................................. ..................................................................
c 19 120 208
2.. d
403 08 0 3060 398
. ..
×
.................................................................. ..................................................................
e 19 080 2082
..
..................................................................
5 A = πr 2 π = 3.142, r = 6.87
Work out an estimate for the value of A.
...........................................................................................................
6 v = ut + 0.5at2 u = 12.66, a = –0.57, t = 21.2
Work out an estimate for the value of v.
...........................................................................................................
7 y 2 = a + bx 2 a = 49.8, b = 0.48, x = 10.1
Work out an estimate for the value of y.
...........................................................................................................
8 h = 3 2Vrπ
π = 3.142, r = 0.891 , V = 9.09
Work out an estimate for the value of h.
...........................................................................................................
C
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�2 3.7 Manipulating decimals
87A
1 Given that 5.6 × 23 = 128.8
work out
a 56 × 23 b 5.6 × 2.3 c 0.56 × 23 d 5.6 × 230
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................................... ...................................
...................................
2 Given that 72 × 48 = 3456
work out
a 7.2 × 48 b 72 × 4800 c 0.72 × 48 d 72 × 4.8
...................................
................................... ...................................
...................................
3 Given that 15.9 × 7.6 = 120.84
work out
a 159 × 7.6 b 159 × 760 c 0.159 × 7.6 d 159 × 0.76
...................................
................................... ...................................
...................................
4 Given that 8.5 ÷ 6.8 = 1.25
work out
a 85 ÷ 6.8 b 0.85 ÷ 6.8 c 8.5 ÷ 68 d 8.5 ÷ 0.68
...................................
................................... ...................................
...................................
5 Given that 151.2 ÷ 6.3 = 24
work out
a 1512 ÷ 6.3 b 151.2 ÷ 63 c 151.2 ÷ 0.063 d 0.1512 ÷ 6.3
...................................
................................... ...................................
...................................
6 Given that 47.97 ÷ 7.8 = 6.15
work out
a 4797 ÷ 7.8 b 47.97 ÷ 780 c 4.797 ÷ 0.78 d 4797 ÷ 78
...................................
................................... ...................................
...................................
Guided practice worksheet
D
Questions are targeted at the grades indicated
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�2 3.7 Manipulating decimals
87B
Guided practice worksheet
7 Given that 5 8 4 914
2 03. . .×× = = 2.03
work out
a 58 49
14××
b 5 8 4 9
1400. .××
c 0 58 490
14. ××
d
58 490140××
...................................
................................... ...................................
...................................
8 Given that 16 2 5 62 1
43 2. ..
.×× =
work out
a 162 56
2 1××
. b 16 2 5 6
210. .××
c
16 2 56210. ××
d
1 62 0 560 021
. ..××
...................................
................................... ...................................
...................................
C