Decimal Fractions

Q1: Convert the following into fractions in their lowest terms:

i. 3.75

Step 1: Write the decimal as a fraction. \[ 3.75 = \frac{375}{100} \] Step 2: Reduce to lowest terms. \[ \frac{375 \div 25}{100 \div 25} = \frac{15}{4} \] Answer: \(\frac{15}{4}\)

ii. 0.5

Step 1: Write as a fraction. \[ 0.5 = \frac{5}{10} \] Step 2: Reduce to lowest terms. \[ \frac{5 \div 5}{10 \div 5} = \frac{1}{2} \] Answer: \(\frac{1}{2}\)

iii. 2.04

Step 1: Write as a fraction. \[ 2.04 = \frac{204}{100} \] Step 2: Reduce to lowest terms. \[ \frac{204 \div 4}{100 \div 4} = \frac{51}{25} \] Answer: \(\frac{51}{25}\)

iv. 0.65

Step 1: Write as a fraction. \[ 0.65 = \frac{65}{100} \] Step 2: Reduce to lowest terms. \[ \frac{65 \div 5}{100 \div 5} = \frac{13}{20} \] Answer: \(\frac{13}{20}\)

v. 2.405

Step 1: Write as a fraction. \[ 2.405 = \frac{2405}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{2405 \div 5}{1000 \div 5} = \frac{481}{200} \] Answer: \(\frac{481}{200}\)

vi. 0.085

Step 1: Write as a fraction. \[ 0.085 = \frac{85}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{85 \div 5}{1000 \div 5} = \frac{17}{200} \] Answer: \(\frac{17}{200}\)

vii. 8.025

Step 1: Write as a fraction. \[ 8.025 = \frac{8025}{1000} \] Step 2: Reduce to lowest terms. \[ \frac{8025 \div 25}{1000 \div 25} = \frac{321}{40} \] Answer: \(\frac{321}{40}\)

Q2: Convert into decimal fractions:

i. \(2\frac{4}{5}\)

Step 1: Convert to improper fraction: \[ 2\frac{4}{5} = \frac{(2 \times 5) + 4}{5} = \frac{14}{5} \] Step 2: Divide numerator by denominator: \[ \frac{14}{5} = 2.8 \] Answer: 2.8

ii. \(\frac{79}{100}\)

Step 1: Divide numerator by denominator: \[ \frac{79}{100} = 0.79 \] Answer: 0.79

iii. \(\frac{37}{10,000}\)

Step 1: Divide numerator by denominator: \[ \frac{37}{10000} = 0.0037 \] Answer: 0.0037

iv. \(\frac{7543}{{10}^4}\)

Step 1: \({10}^4 = 10000\) \[ \frac{7543}{10000} = 0.7543 \] Answer: 0.7543

v. \(\frac{3}{4}\)

Step 1: Divide numerator by denominator: \[ \frac{3}{4} = 0.75 \] Answer: 0.75

vi. \(9\frac{3}{5}\)

Step 1: Convert to improper fraction: \[ 9\frac{3}{5} = \frac{(9 \times 5) + 3}{5} = \frac{48}{5} \] Step 2: Divide numerator by denominator: \[ \frac{48}{5} = 9.6 \] Answer: 9.6

vii. \(8\frac{5}{8}\)

Step 1: Convert to improper fraction: \[ 8\frac{5}{8} = \frac{(8 \times 8) + 5}{8} = \frac{69}{8} \] Step 2: Divide numerator by denominator: \[ \frac{69}{8} = 8.625 \] Answer: 8.625

viii. \(5\frac{7}{8}\)

Step 1: Convert to improper fraction: \[ 5\frac{7}{8} = \frac{(5 \times 8) + 7}{8} = \frac{47}{8} \] Step 2: Divide numerator by denominator: \[ \frac{47}{8} = 5.875 \] Answer: 5.875

Q3: Write the number of decimal places in:

i. \(0.4762\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 0.4762 = 4 \] Answer: 4 decimal places

ii. \(7.00349\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 7.00349 = 5 \] Answer: 5 decimal places

iii. \(8235.403\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 8235.403 = 3 \] Answer: 3 decimal places

iv. \(35.4\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 35.4 = 1 \] Answer: 1 decimal place

v. \(2.608\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 2.608 = 3 \] Answer: 3 decimal places

vi. \(0.000879\)

Step 1: Count digits after the decimal point. \[ \text{Digits after decimal in } 0.000879 = 6 \] Answer: 6 decimal places

Q4: Write the following decimals as word statements:

i. \(0.4, 0.9, 0.1\)

Step 1: Express each decimal as “zero-point-” followed by digits read individually.

• \(0.4\) — zero-point-four
• \(0.9\) — zero-point-nine
• \(0.1\) — zero-point-one

Answer: zero-point-four, zero-point-nine, zero-point-one

ii. \(1.9, 4.4, 7.5\)

Step 1: Read the whole number, then say “point” followed by digits individually.

• \(1.9\) — one-point-nine
• \(4.4\) — four-point-four
• \(7.5\) — seven-point-five

Answer: one-point-nine, four-point-four, seven-point-five

iii. \(0.02, 0.56, 13.06\)

Step 1: Read as zero-point- for decimals less than 1 and whole number with point for others.

• \(0.02\) — zero-point-zero-two
• \(0.56\) — zero-point-five-six
• \(13.06\) — thirteen-point-zero-six

Answer: zero-point-zero-two, zero-point-five-six, thirteen-point-zero-six

iv. \(0.005, 0.207, 111.519\)

Step 1: Read digit-by-digit after decimal, starting with zero-point- for decimals less than 1.

• \(0.005\) — zero-point-zero-zero-five
• \(0.207\) — zero-point-two-zero-seven
• \(111.519\) — one hundred eleven-point-five-one-nine

Answer: zero-point-zero-zero-five, zero-point-two-zero-seven, one hundred eleven-point-five-one-nine

v. \(0.8, 0.08, 0.008, 0.0008\)

Step 1: Use zero-point- and read every digit after decimal individually.

• \(0.8\) — zero-point-eight
• \(0.08\) — zero-point-zero-eight
• \(0.008\) — zero-point-zero-zero-eight
• \(0.0008\) — zero-point-zero-zero-zero-eight

Answer: zero-point-eight, zero-point-zero-eight, zero-point-zero-zero-eight, zero-point-zero-zero-zero-eight

vi. \(256.1, 10.22, 0.634\)

Step 1: Read the whole number, then “point” followed by digits individually.

• \(256.1\) — two hundred fifty-six-point-one
• \(10.22\) — ten-point-two-two
• \(0.634\) — zero-point-six-three-four

Answer: two hundred fifty-six-point-one, ten-point-two-two, zero-point-six-three-four

Q5: Convert the given fractions into like fractions:

i. \(0.5, 3.62, 43.981, \text{ and } 232.0037\)

Step 1: Find the decimal with the greatest number of decimal places. \[ 0.5 = 0.5 \quad (\text{1 decimal place}) \\ 3.62 = 3.62 \quad (\text{2 decimal places}) \\ 43.981 = 43.981 \quad (\text{3 decimal places}) \\ 232.0037 = 232.0037 \quad (\text{4 decimal places}) \]Step 2: Convert all decimals to have the same number of decimal places (4 decimal places, as in 232.0037) by adding zeros. \[ 0.5 = 0.5000 \\ 3.62 = 3.6200 \\ 43.981 = 43.9810 \\ 232.0037 = 232.0037 \]Answer: 0.5000, 3.6200, 43.9810, 232.0037

ii. \(215.78, 33.0006, 530.3, \text{ and } 0.03569\)

Step 1: Find the decimal with the greatest number of decimal places. \[ 215.78 = 215.78 \quad (\text{2 decimal places}) \\ 33.0006 = 33.0006 \quad (\text{4 decimal places}) \\ 530.3 = 530.3 \quad (\text{1 decimal place}) \\ 0.03569 = 0.03569 \quad (\text{5 decimal places}) \]Step 2: Convert all decimals to have the same number of decimal places (5 decimal places, as in 0.03569) by adding zeros. \[ 215.78 = 215.78000 \\ 33.0006 = 33.00060 \\ 530.3 = 530.30000 \\ 0.03569 = 0.03569 \\ \]Answer: 215.78000, 33.00060, 530.30000, 0.03569