Exercise: 5-C
Q1: Convert each of the following decimals into a fraction with lowest terms:
i. 0.8
Step 1: 0.8 = \(\frac{8}{10}\)
Step 2: Simplify: \(\frac{8}{10} = \frac{4}{5}\)
Answer: \(\frac{4}{5}\)
ii. 0.06
Step 1: 0.06 = \(\frac{6}{100}\)
Step 2: Simplify: \(\frac{6}{100} = \frac{3}{50}\)
Answer: \(\frac{3}{50}\)
iii. 0.45
Step 1: 0.45 = \(\frac{45}{100}\)
Step 2: Simplify: \(\frac{45}{100} = \frac{9}{20}\)
Answer: \(\frac{9}{20}\)
iv. 0.64
Step 1: 0.64 = \(\frac{64}{100}\)
Step 2: Simplify: \(\frac{64}{100} = \frac{16}{25}\)
Answer: \(\frac{16}{25}\)
v. 5.4
Step 1: 5.4 = \(\frac{54}{10} = \frac{27}{5} = 5\frac{2}{5}\)
Answer: \(5\frac{2}{5}\)
vi. 6.25
Step 1: 6.25 = \(\frac{625}{100} = \frac{25}{4} = 6\frac{1}{4}\)
Answer: \(6\frac{1}{4}\)
vii. 8.125
Step 1: 8.125 = \(\frac{8125}{1000}\)
Step 2: Simplify: \(\frac{8125 \div 125}{1000 \div 125} = \frac{65}{8} = 8\frac{1}{8}\)
Answer: \(8\frac{1}{8}\)
viii. 3.475
Step 1: 3.475 = \(\frac{3475}{1000}\)
Step 2: Simplify: \(\frac{3475 \div 25}{1000 \div 25} = \frac{139}{40} = 3\frac{19}{40}\)
Answer: \(3\frac{19}{40}\)
Q2: Convert each of the following fractions into a decimal:
i. \(\frac{9}{10}\)
Step 1: Divide 9 by 10: \(9 \div 10 = 0.9\)
Answer: 0.9
ii. \(\frac{23}{10}\)
Step 1: Divide 23 by 10: \(23 \div 10 = 2.3\)
Answer: 2.3
iii. \(\frac{427}{10}\)
Step 1: Divide 427 by 10: \(427 \div 10 = 42.7\)
Answer: 42.7
iv. \(\frac{37}{100}\)
Step 1: Divide 37 by 100: \(37 \div 100 = 0.37\)
Answer: 0.37
v. \(\frac{107}{100}\)
Step 1: Divide 107 by 100: \(107 \div 100 = 1.07\)
Answer: 1.07
vi. \(\frac{1423}{100}\)
Step 1: Divide 1423 by 100: \(1423 \div 100 = 14.23\)
Answer: 14.23
vii. \(\frac{123}{1000}\)
Step 1: Divide 123 by 1000: \(123 \div 1000 = 0.123\)
Answer: 0.123
viii. \(\frac{2045}{1000}\)
Step 1: Divide 2045 by 1000: \(2045 \div 1000 = 2.045\)
Answer: 2.045
Q3: Convert each of the following fractions into a decimal:
i. \(\frac{3}{20}\)
Step 1: Divide 3 by 20: \(3 \div 20 = 0.15\)
Answer: 0.15
ii. \(\frac{7}{25}\)
Step 1: Divide 7 by 25: \(7 \div 25 = 0.28\)
Answer: 0.28
iii. \(\frac{9}{50}\)
Step 1: Divide 9 by 50: \(9 \div 50 = 0.18\)
Answer: 0.18
iv. \(\frac{1}{4}\)
Step 1: Divide 1 by 4: \(1 \div 4 = 0.25\)
Answer: 0.25
v. \(\frac{16}{125}\)
Step 1: Divide 16 by 125: \(16 \div 125 = 0.128\)
Answer: 0.128
vi. \(\frac{231}{250}\)
Step 1: Divide 231 by 250: \(231 \div 250 = 0.924\)
Answer: 0.924
vii. \(\frac{17}{500}\)
Step 1: Divide 17 by 500: \(17 \div 500 = 0.034\)
Answer: 0.034
viii. \(\frac{8}{250}\)
Step 1: Simplify first: \(\frac{8}{250} = \frac{4}{125}\)
Step 2: Now divide: \(4 \div 125 = 0.032\)
Answer: 0.032
Q4: Convert each of the following fractions into a decimal:
i. \(5\frac{3}{4}\)
Step 1: Convert to improper fraction: \(\frac{(5 \times 4 + 3)}{4} = \frac{23}{4}\)
Step 2: Divide 23 by 4: \(23 \div 4 = 5.75\)
Answer: 5.75
ii. \(3\frac{1}{4}\)
Step 1: \(\frac{(3 \times 4 + 1)}{4} = \frac{13}{4}\)
Step 2: \(13 \div 4 = 3.25\)
Answer: 3.25
iii. \(6\frac{1}{5}\)
Step 1: \(\frac{(6 \times 5 + 1)}{5} = \frac{31}{5}\)
Step 2: \(31 \div 5 = 6.2\)
Answer: 6.2
iv. \(12\frac{4}{5}\)
Step 1: \(\frac{(12 \times 5 + 4)}{5} = \frac{64}{5}\)
Step 2: \(64 \div 5 = 12.8\)
Answer: 12.8
v. \(7\frac{3}{8}\)
Step 1: \(\frac{(7 \times 8 + 3)}{8} = \frac{59}{8}\)
Step 2: \(59 \div 8 = 7.375\)
Answer: 7.375
vi. \(2\frac{4}{25}\)
Step 1: \(\frac{(2 \times 25 + 4)}{25} = \frac{54}{25}\)
Step 2: \(54 \div 25 = 2.16\)
Answer: 2.16
vii. \(3\frac{7}{20}\)
Step 1: \(\frac{(3 \times 20 + 7)}{20} = \frac{67}{20}\)
Step 2: \(67 \div 20 = 3.35\)
Answer: 3.35
viii. \(4\frac{11}{20}\)
Step 1: \(\frac{(4 \times 20 + 11)}{20} = \frac{91}{20}\)
Step 2: \(91 \div 20 = 4.55\)
Answer: 4.55
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