Exercise: 3-A
Q1: Convert the following decimals into like decimals:
i. 8.1, 9.4, 6.05, 12
Step 1: Find the decimal places in each number
8.1 → 1 decimal place
9.4 → 1 decimal place
6.05 → 2 decimal places
12 → 0 decimal places
Step 2: Convert all numbers to have equal decimal places (maximum is 2)
⇒ 8.1 = 8.10
⇒ 9.4 = 9.40
⇒ 6.05 = 6.05
⇒ 12 = 12.00
Answer: 8.10, 9.40, 6.05, 12.00
ii. 6.35, 11.8, 9.125, 32.04, 9
Step 1: Decimal places
6.35 → 2 d.p.
11.8 → 1 d.p.
9.125 → 3 d.p.
32.04 → 2 d.p.
9 → 0 d.p.
Step 2: Max decimal places = 3
⇒ 6.35 = 6.350
⇒ 11.8 = 11.800
⇒ 9.125 = 9.125
⇒ 32.04 = 32.040
⇒ 9 = 9.000
Answer: 6.350, 11.800, 9.125, 32.040, 9.000
iii. 6.005, 2, 0.6, 1.78, 14.3
Step 1: Decimal places
6.005 → 3 d.p.
2 → 0 d.p.
0.6 → 1 d.p.
1.78 → 2 d.p.
14.3 → 1 d.p.
Step 2: Max decimal places = 3
⇒ 6.005 = 6.005
⇒ 2 = 2.000
⇒ 0.6 = 0.600
⇒ 1.78 = 1.780
⇒ 14.3 = 14.300
Answer: 6.005, 2.000, 0.600, 1.780, 14.300
iv. 0.72, 53.7, 16, 8.304, 2.3754
Step 1: Decimal places
0.72 → 2 d.p.
53.7 → 1 d.p.
16 → 0 d.p.
8.304 → 3 d.p.
2.3754 → 4 d.p.
Step 2: Max decimal places = 4
⇒ 0.72 = 0.7200
⇒ 53.7 = 53.7000
⇒ 16 = 16.0000
⇒ 8.304 = 8.3040
⇒ 2.3754 = 2.3754
Answer: 0.7200, 53.7000, 16.0000, 8.3040, 2.3754
Q2: Write each of the following decimals into expanded form:
i. 16.74
\[
16.74 = 10 + 6 + \frac{7}{10} + \frac{4}{100}
\]Answer: \(10 + 6 + \frac{7}{10} + \frac{4}{100}\)
ii. 243.689
\[
243.689 = 200 + 40 + 3 + \frac{6}{10} + \frac{8}{100} + \frac{9}{1000}
\]Answer: \(200 + 40 + 3 + \frac{6}{10} + \frac{8}{100} + \frac{9}{1000}\)
iii. 9.3578
\[
9.3578 = 9 + \frac{3}{10} + \frac{5}{100} + \frac{7}{1000} + \frac{8}{10000}
\]Answer: \(9 + \frac{3}{10} + \frac{5}{100} + \frac{7}{1000} + \frac{8}{10000}\)
iv. 2314.57
\[
2314.57 = 2000 + 300 + 10 + 4 + \frac{5}{10} + \frac{7}{100}
\]Answer: \(2000 + 300 + 10 + 4 + \frac{5}{10} + \frac{7}{100}\)
Q3: Express each of the following as a fraction in simplest form:
i. 0.8
\[
0.8 = \frac{8}{10} = \frac{4}{5}
\]Answer: \(\frac{4}{5}\)
ii. 0.45
\[
0.45 = \frac{45}{100} = \frac{9}{20}
\]Answer: \(\frac{9}{20}\)
iii. 1.6
\[
1.6 = \frac{16}{10} = \frac{8}{5} = 1\frac{3}{5}
\]Answer: \(1\frac{3}{5}\)
iv. 4.75
\[
4.75 = \frac{475}{100} = \frac{19}{4} = 4\frac{3}{4}
\]Answer: \(4\frac{3}{4}\)
v. 0.345
\[
0.345 = \frac{345}{1000} = \frac{69}{200}
\]Answer: \(\frac{69}{200}\)
vi. 64.015
\[
64.015 = \frac{64015}{1000} = \frac{12803}{200} = 64\frac{3}{200}
\]Answer: \(64\frac{3}{200}\)
vii. 12.725
\[
12.725 = \frac{12725}{1000} = \frac{509}{40} = 12\frac{29}{40}
\]Answer: \(12\frac{29}{40}\)
viii. 0.0024
\[
0.0024 = \frac{24}{10000} = \frac{3}{1250}
\]Answer: \(\frac{3}{1250}\)
Q4: Convert each of the following fractions into a decimal:
i. \(\frac{19}{10}\)
\[
\frac{19}{10} = 1.9
\]Answer: 1.9
ii. \(\frac{243}{100}\)
\[
\frac{243}{100} = 2.43
\]Answer: 2.43
iii. \(\frac{51}{100}\)
\[
\frac{51}{100} = 0.51
\]Answer: 0.51
iv. \(\frac{9}{100}\)
\[
\frac{9}{100} = 0.09
\]Answer: 0.09
v. \(\frac{72}{1000}\)
\[
\frac{72}{1000} = 0.072
\]Answer: 0.072
vi. \(\frac{3}{5}\)
5 ) 3.0000 (0.6000
-2.500
--------
50
- 50
--------
0
Answer: 0.6
vii. \(\frac{7}{8}\)
8 ) 7.0000 (0.8750
- 64
-----
60
- 56
-----
40
- 40
-----
0
Answer: 0.875
viii. \(\frac{37}{40}\)
40 ) 37.0000 (0.9250
- 320
------
270
- 240
------
300
- 280
------
0
Answer: 0.925
ix. \(4\frac{3}{8}\)
8 ) 35.0000 (4.375
-32
-----
30
- 24
-----
60
- 56
-----
40
- 40
-----
0
Answer: 4.375
x. \(9\frac{1}{25}\)
25 ) 226.0000 (9.04
- 200
--------
26
- 00
--------
260
- 250
--------
0
Answer: 9.04
xi. \(2\frac{9}{16}\)
16 ) 41.0000 (2.5625
- 32
--------
90
- 80
--------
100
- 96
--------
40
- 32
--------
80
- 80
--------
0
Answer: 2.5625
xii. \(4\frac{11}{125}\)
125 ) 511.0000 (4.0880
- 500
--------
110
- 000
--------
1100
- 1000
--------
1000
- 1000
--------
0
Answer: 4.088
