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Percentages Þ Decimals
Percentages Ü Decimals
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• To convert a decimal into a percentage, we multiply
the decimal by 100
• To convert a percentage into a decimal, we divide
the percentage by 100
÷ 100
0.3
x 100
30%
23%
0.75
x 100
75%
1%
÷ 100
0.01
0.34
x 100
34%
250%
÷ 100
2.5
0.05
x 100
5%
17.5% ÷ 100
1.5
x 100
150%
46.5%
0.325
x 100
32.5% 0.5%
0.23
0.175
÷ 100
0.465
÷ 100
0.005
© T Madas
Decimals
c
Percentages
[Quick Test]
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Percentages & Decimals
30% = 0.3
33% = 0.33
13.2% = 0.132
60% = 0.6
87% = 0.87
12.3% = 0.123
90% = 0.9
11% = 0.11
76.5% = 0.765
10% = 0.1
32% = 0.32
62.9% = 0.629
55% = 0.55
6% = 0.06
150% = 1.5
35% = 0.35
1% = 0.01
500% = 5
85% = 0.85
8% = 0.08
2.5% = 0.025
25% = 0.25
17.5% = 0.175
6.5% = 0.065
5% = 0.05
22.5% = 0.225
0.5% = 0.005
© T Madas
Percentages & Decimals
20% = 0.2
73% = 0.73
63.2% = 0.632
50% = 0.5
47% = 0.47
19.3% = 0.193
80% = 0.8
21% = 0.21
46.5% = 0.465
40% = 0.4
38% = 0.38
92.9% = 0.929
65% = 0.65
4% = 0.04
250% = 2.5
95% = 0.95
1% = 0.01
300% = 3
15% = 0.15
9% = 0.09
7.5% = 0.075
75% = 0.75
87.5% = 0.875
6.1% = 0.061
5% = 0.05
27.5% = 0.275
0.5% = 0.005
© T Madas
Percentages Þ Fractions
Percentages Ü Fractions
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To change a percentage into a fraction we write a fraction
with numerator the same as the percentage, and with
denominator equal to 100.
We then cancel it down.
1
10
=
10 % =
10
100
11
55
=
55 % =
20
100
3
30
=
30 % =
10
100
3
12
=
12 % =
25
100
1
25
=
25 % =
4
100
4
40
2
=
=
40% =
10
100
5
7
14
=
14 % =
50
100
33
33 % =
100
© T Madas
To change some fractions into a percentage, we try to find
an equivalent fraction out of 100.
The numerator of a fraction out of 100 is the percentage.
x2
11
22 = 22%
=
50 100
x5
7
35 = 35%
=
20 100
x 20
2
40 = 40%
=
5
100
x2
x5
x 20
x 10
x4
x 25
3
30 = 30%
=
10 100
x 10
6
24 = 24%
=
25 100
x4
5
125 = 125%
=
4
100
x 25
© T Madas
Changing Fractions
into
Percentages
[Quick Test]
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Change these fractions into percentages
3
30 = 30%
=
10 100
3 150
= 150%
=
2 100
3
6
= 6%
=
50 100
1
25 = 25%
=
4 100
1
20 = 20%
=
5 100
3
15 = 15%
=
20 100
3
60 = 60%
=
5 100
11
15 = 55%
=
20 100
10
40 = 40%
=
25 100
7
28 = 28%
=
25 100
© T Madas
• To convert a decimal into a percentage, we multiply the
decimal by 100
• To convert a percentage into a decimal, we divide the
percentage by 100
To change a percentage into
a fraction we write a fraction
with numerator the same as
the percentage, and with
denominator equal to 100.
We then cancel it down.
E.g. 60% = 60 = 6 = 3
100 10 5
To change some fractions into
a percentage, we try to find
an equivalent fraction out of
100.
The numerator of a fraction
out of 100 is the percentage.
E.g.
x5
7 = 35 = 35%
20x5 100
To change any fraction into a percentage, we change the
fraction into a decimal (by division if necessary) and change the
decimal into a percentage.
© T Madas
© T Madas
What percentage of the bar is shaded?
1
= 10%
10
1
= 25%
4
1
= 12.5%
8
1
= 20%
5
1
= 5%
20
1
= 33⅓%
3
© T Madas
What percentage of the bar is shaded?
3
= 30%
10
1
= 50%
2
3
= 37.5%
8
4
= 80%
5
3
= 15%
20
1
= 33⅓%
3
© T Madas
What percentage of the bar is shaded?
7
= 70%
10
3
= 75%
4
1
= 12.5%
8
3
= 60%
5
7
= 35%
20
2
= 66⅔%
3
© T Madas
What percentage of the bar is shaded?
9
= 90%
10
2
= 40%
5
5
= 62.5%
8
9
= 45%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
What percentage of the bar is shaded?
6
= 60%
10
4
= 80%
5
3
= 37.5%
8
11
= 55%
20
2
= 66⅔%
3
2
= 33 1 3 %
6
© T Madas
What percentage of the bar is shaded?
8
= 60%
10
3
= 60%
5
7
= 87.5%
8
13
= 65%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
What percentage of the bar is shaded?
5
= 50%
10
2
= 40%
5
1
= 12.5%
8
17
= 85%
20
2
= 66⅔%
3
very hard
5
= 83 1 3 %
6
© T Madas
What percentage of the bar is shaded?
8
= 80%
10
1
= 20%
5
3
= 37.5%
8
19
= 95%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
© T Madas
What percentage of the bar is shaded?
1
= 10%
10
1
= 25%
4
1
= 12.5%
8
1
= 20%
5
1
= 5%
20
1
= 33⅓%
3
© T Madas
What percentage of the bar is shaded?
3
= 30%
10
1
= 50%
2
3
= 37.5%
8
4
= 80%
5
3
= 15%
20
1
= 33⅓%
3
© T Madas
What percentage of the bar is shaded?
7
= 70%
10
3
= 75%
4
1
= 12.5%
8
3
= 60%
5
7
= 35%
20
2
= 66⅔%
3
© T Madas
What percentage of the bar is shaded?
9
= 90%
10
2
= 40%
5
5
= 62.5%
8
9
= 45%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
What percentage of the bar is shaded?
6
= 60%
10
4
= 80%
5
3
= 37.5%
8
11
= 55%
20
2
= 66⅔%
3
2
= 33 1 3 %
6
© T Madas
What percentage of the bar is shaded?
8
= 60%
10
3
= 60%
5
7
= 87.5%
8
13
= 65%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
What percentage of the bar is shaded?
5
= 50%
10
2
= 40%
5
1
= 12.5%
8
17
= 85%
20
2
= 66⅔%
3
very hard
5
= 83 1 3 %
6
© T Madas
What percentage of the bar is shaded?
8
= 80%
10
1
= 20%
5
3
= 37.5%
8
19
= 95%
20
1
= 33⅓%
3
hard
1
= 16 2 3 %
6
© T Madas
© T Madas
0.5
50%
0.25 25%
0.1
10%
0.75 75%
0.3
30%
0.05 5%
0.2
20%
0.15 15%
1
2
1
4
1
10
3
4
3
10
1
20
1
5
3
20
0.4
40%
0.9
90%
0.35 35%
0.12 12%
0.44 44%
0.01 1%
0.06 6%
0.125 12.5%
2
5
9
10
7
20
3
25
11
25
1
100
3
50
1
8
© T Madas
0.2
20%
0.72 72%
0.55 55%
0.8
80%
0.22 22%
0.04 4%
0.24 24%
0.125 12.5%
1
5
18
25
11
20
4
5
11
50
1
25
6
25
1
8
0.6
40%
0.7
70%
0.45 45%
0.18 18%
0.32 32%
0.03 3%
0.14 14%
0.375 37.5%
3
5
7
10
9
20
9
50
8
25
3
100
7
50
3
8
© T Madas
0.2
20%
0.48 48%
0.65 65%
0.125 12.5%
0.34 34%
0.08 8%
0.54 54%
0.625 62.5%
1
5
12
25
13
20
1
8
17
50
2
25
27
50
5
8
0.8
80%
0.91 91%
0.85 85%
0.38 38%
0.28 28%
0.07 7%
0.42 42%
0.875 87.5%
4
5
91
100
17
20
19
50
7
25
7
100
21
50
7
8
© T Madas
© T Madas
0.5
50%
0.25 25%
0.1
10%
0.75 75%
0.3
30%
0.05 5%
0.2
20%
0.15 15%
1
2
1
4
1
10
3
4
3
10
1
20
1
5
3
20
0.4
40%
0.9
90%
0.35 35%
0.12 12%
0.44 44%
0.01 1%
0.06 6%
0.125 12.5%
2
5
9
10
7
20
3
25
11
25
1
100
3
50
1
8
© T Madas
0.2
20%
0.72 72%
0.55 55%
0.8
80%
0.22 22%
0.04 4%
0.24 24%
0.125 12.5%
1
5
18
25
11
20
4
5
11
50
1
25
6
25
1
8
0.6
40%
0.7
70%
0.45 45%
0.18 18%
0.32 32%
0.03 3%
0.14 14%
0.375 37.5%
3
5
7
10
9
20
9
50
8
25
3
100
7
50
3
8
© T Madas
0.2
20%
0.48 48%
0.65 65%
0.125 12.5%
0.34 34%
0.08 8%
0.54 54%
0.625 62.5%
1
5
12
25
13
20
1
8
17
50
2
25
27
50
5
8
0.8
80%
0.91 91%
0.85 85%
0.38 38%
0.28 28%
0.07 7%
0.42 42%
0.875 87.5%
4
5
91
100
17
20
19
50
7
25
7
100
21
50
7
8
© T Madas
© T Madas
The table below shows which foreign language did pupils prefer
to learn.
1.Which language did 10% of the girls prefer?
2.Which language did 45% of the boys prefer?
3.Which language was equally preferred by boys and girls?
Language
Boys
Girls
French
3 15%
1 10%
German
9 45%
3 30%
Italian
4 20%
2 20%
Spanish
4 20%
4 40%
TOTAL
20
10
x 10
1
10
= 10%
=
10
100
x 10
x5
3
15
= 15%
=
20
100
x5
x5
9
45
= 45%
=
20
100
x5
x5
4
20
= 20%
=
20
100
x5
© T Madas
© T Madas
Riaz got the following marks in his end of year exams:
• English: 37
50
• Science: 17
25
• Maths: 17
20
• History: 21
30
Change these marks into percentages
x2
x5
English: 37 = 74 = 74%
50
100
x2
Maths: 17 = 85 = 85%
20
x4
÷3
x 10
÷3
x 10
Science: 17 = 68 = 68%
25
100
x4
x5
100
Science: 21 = 7 = 70 = 70%
30
100
10
© T Madas
© T Madas