Decimals

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