# Yr7-FractionsDecimals ```Year 7 Fractions, Decimal,
Percentages
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com
Objectives: Convert between fractions, decimals and percentages,
including fractions to recurring decimals. Be able to order fractions.
www.drfrostmaths.com
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RECAP :: Basic Decimal-Fraction conversions
Fraction Decimal Percentage
1
2
1
4
3
?
4
2
?5
7
10
1
8
7
8
7
?
20
0.5
50%
?
0.25
?
25%
?
Fill in the table with the missing
decimals/fractions/%s, and
place the fractions all on a single
number line as pictured.
0.75
75%
?
(Copying note: don’t waste time drawing
lots of lines for your table!)
0.4
40%
?
0.7
?
70%
?
0.125
?
12.5%
?
0.875
?
87.5%
?
0.35
35%
?
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
8
1 72
4 20 5
1
2
73
10 4
7
8
Ordering
[JMC 2002 Q15] In which of the following lists are the terms not increasing?
1
3
3
4
2
7
A , 0.25, , 0.5
B , 0.7, , 1.5
C , 0.5, , 0.9
D
5
10
3
4
, 0.5, , 0.9
5
5
E
A
B
5
5
2
10
, 1.5, , 2.3
5
5
C
5
D
10
E
[JMC 1998 Q11] Which is the smallest of these fractions?
5
6
7
9
A
B
C
D
8
13
A
B
12
C
E
17
D
10
19
E
[JMC 2005 Q14] If the following fractions are arranged in increasing order of
size, which one is in the middle?
1
2
3
4
5
A
B
C
D
E
2
3
A
5
B
C
7
D
9
E
Decimals → Fractions
Is there a method for converting any arbitrary decimal to a fraction?
45
9
0.45 = ? = ?
100 20
We used hundred because
the last digit was the
hundredths digit.
255
51
0.255 = ? = ?
1000 200
85
17
0.85 = ? = ?
100 20
126
63
0.126 = ? = ?
1000 500
612
153
0.612 = ? = ?
1000 250
16
4
0.16 = ? = ?
100 25
5
1
0.0005 = ?
= ?
10000 2000
𝟑
?
0.03 =
𝟏𝟎𝟎
𝟕
?
0.007 =
𝟏𝟎𝟎𝟎
𝟖
𝟐
0.08 =
=?
𝟏𝟎𝟎 𝟐𝟓
𝟏𝟓
𝟑
?
0.015 =
=
𝟏𝟎𝟎𝟎 𝟐𝟎𝟎
N
If that’s too easy:
𝟏𝟎𝟎𝒂 + 𝒃
0. 𝑎0𝑏 =
?
𝟏𝟎𝟎𝟎
Fractions → Decimals
3
8
just means 3 &divide; 8. So we could use long division to convert it
to a decimal.
8
0 . 3 7 5
3 . 30 6 0 40
Uh oh. We’ve run out of digits and hence have
nowhere to put the remainder. What can we
do to the 3 without changing its value?
Fractions → Decimals
4
= 0. 36
11
11
0 . 3 6 3 6
4 . 40 7 0 40 70
Use of recurring dot
What do the following represent?
? …
0. 2 = 0.22222222
?
0.315 = 0.315555555
…
?
0. 315 = 0.315315315
…
?
0.315 = 0.315151515
…
7
= 0.4? 6
15
5
?
= 0. 5
9
6
?
= 0. 85714
2
7
Exercise 1
1
a
What are the following decimals as
fractions in their simplest form?
𝟖
𝟗
e 0.9 = ?
0.32 = 𝟐𝟓?
𝟏𝟎
𝟏𝟑
0.65 = 𝟐𝟎?
f
0.04 = 𝟐𝟓
?
c
0.312 = 𝟏𝟐𝟓
?
g
0.888 = 𝟏𝟐𝟓
?
d
0.325 = 𝟒𝟎
?
h
0.998 = 𝟓𝟎𝟎
?
2
Put the following numbers in
ascending order:
7
9
c 1 , 3 , 0.12, 1
,
0.85,
8
10
5 20
9
a
b
𝟏𝟑
3
29
,
0.715,
4
40
d
𝟏𝟏𝟏
Convert the fractions to (potentially
recurring) decimals.
a 1 = 𝟎. 𝟎
d 2 = 𝟎. 𝟐?
𝟗
?
11
9
3
2
e = 𝟎. 𝟐𝟖𝟓𝟕𝟏
b
?
? 𝟒
= 𝟎. 𝟏𝟖𝟕𝟓
3
c
16
33
13
7
= 𝟐. 𝟓𝟑𝟖𝟒𝟔
? 𝟏 f
5
𝟒𝟗𝟗
1
3 3
,
0.33,
,
3
10 8
102
101
= 𝟏. 𝟎𝟎𝟗
?𝟗
[JMC 2009 Q9] How many different digits appear
20
when is written as a recurring decimal?
11
A 2
B 3
C 4
D 5
E 6
Solution: A
?
𝟏
b
𝟑𝟗
4
[JMO 2001 A5] Find the 100th digit after the
3
decimal point in the decimal representation of .
7
Solution: 5
?
6
[IMC 2008 Q18] When the following values are
put in ascending order, which is in the middle?
A 0.2008 B 0.2008 C 0.2008
D 0.2008 E 0. 2008
Solution: C
?
7
[Kangaroo Pink 2009 Q15] Which of these
2009
20009
decimals is less than
but greater than
?
2008
20008
A 1.01 B 1.001 C 1.0001
D 1.00001
E 1.000001
Solution: C.
𝟐𝟎𝟎𝟗
𝟐𝟎𝟎𝟖
=𝟏
𝟏
𝟐𝟎𝟎𝟖
. Since 2008 &gt; 2000, this is
?
slightly less than 1.0005. Similarly
1
𝟏
𝟐𝟎𝟎𝟎𝟎
= 𝟏. 𝟎𝟎𝟎𝟎𝟓.
𝟐𝟎𝟎𝟎𝟗
𝟐𝟎𝟎𝟎𝟖
=𝟏
𝟏
𝟐𝟎𝟎𝟎𝟖
.
```