mathematics and busienss

1. Year 7 Fractions, Decimal,
Percentages
Dr J Frost (jfrost@tiffin.kingston.sch.uk)
www.drfrostmaths.com
Last modified: 2nd
February 2016
Objectives: Convert between fractions, decimals and percentages,
including fractions to recurring decimals. Be able to order fractions.

2. RECAP :: Basic Decimal-Fraction conversions
Fill in the table with the missing
decimals/fractions/%s, and
place the fractions all on a single
number line as pictured.
(Copying note: don’t waste time drawing
lots of lines for your table!)
Fraction Decimal Percentage
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
1
2
1
4
3
4
2
5
7
10
1
8
7
8
7
20
?
? ?
? ?
? ?
? ?
? ?
? ?
? ?

3. Ordering
[JMC 2002 Q15] In which of the following lists are the terms not increasing?
A B C
D E
D
B
A C E
[JMC 1998 Q11] Which is the smallest of these fractions?
A B C D E
B D
A C E
[JMC 2005 Q14] If the following fractions are arranged in increasing order of
size, which one is in the middle?
A B C D E
D
B
A C E
Bro Tip: Picture a number line in your head.

4. Decimals Fractions
Is there a method for converting any arbitrary decimal to a fraction?
0.45=
45
100
=
9
20
We used hundred because
the last digit was the
hundredths digit.
? ?
0.126=
12 6
1000
=
63
500
0.16=
16
100
=
4
25
0.255=
255
1000
=
51
200
0.612=
612
1000
=
153
250
0.0005=
5
10000
=
1
2000
? ?
? ?
0.85=
85
100
=
17
20
? ?
? ?
? ?
? ?

5. Check Your Understanding
0.03=
𝟑
𝟏𝟎𝟎
If that’s too easy:
N
?
?
?
?
?

6. Fractions Decimals
just means . So we could use long division to convert it to a
decimal.
3
8
0
. 3
0
. 3
6
0
7
4
0
5
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?

7. Fractions Decimals
4
11
4
11
0
. 4
0
. 3
7
0
6
4
0
3
7
0
6
¿ 0. 3̇ 6̇

8. Use of recurring dot
What do the following represent?
0.2̇=0.22222222…
?
?
?
?

9. Check Your Understanding
5
9
=0.5̇
6
7
=0. 8̇ 5714 2̇
?
7
15
=0.4 6̇
?
?

10. Exercise 1
[JMC 2009 Q9] How many different digits appear
when is written as a recurring decimal?
A 2 B 3 C 4 D 5 E 6
Solution: A
[JMO 2001 A5] Find the 100th
digit after the
decimal point in the decimal representation of .
Solution: 5
[IMC 2008 Q18] When the following values are
put in ascending order, which is in the middle?
A B C
D E Solution: C
[Kangaroo Pink 2009 Q15] Which of these
decimals is less than but greater than ?
A 1.01 B 1.001 C 1.0001
D 1.00001 E 1.000001
Solution: C. . Since 2008 > 2000, this is slightly less
than 1.0005. Similarly . 1.
What are the following decimals as
fractions in their simplest form?
Put the following numbers in
ascending order:
Convert the fractions to (potentially
recurring) decimals.
1
2
3
4
5
6
7
a e
b
c
d
f
g
h
a
b
c
d
a d
b
c
e
f
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