Question

Write each of the following fractions as a terminating decimal or, if a repeating decimal, rounded to the thousandths place. a. \(\frac{6}{5}\) b. \(\frac{9}{25}\) c. \(\frac{5}{24}\) d. \(\frac{1}{8}\) e.\(\frac{3}{20}\) f. \(2 \frac{5}{6}\) g. \(\frac{3}{7}\) h. \(\frac{11}{8}\)

Short answer

Question: Convert the following fractions into decimals rounded to the thousandths place. a. \(\frac{6}{5}\) b. \(\frac{9}{25}\) c. \(\frac{5}{24}\) d. \(\frac{1}{8}\) e. \(\frac{3}{20}\) f. \(2 \frac{5}{6}\) g. \(\frac{3}{7}\) h. \(\frac{11}{8}\) Answer: a. 1.2 b. 0.36 c. 0.208 d. 0.125 e. 0.15 f. 2.833 g. 0.429 h. 1.375

Step-by-step solution

a. Convert \(\frac{6}{5}\) to decimal

Divide the numerator (6) by the denominator (5): \(6 \div 5 = 1.2\). Since this is already a terminating decimal, there is no need to round. So, \(\frac{6}{5} = 1.2\).

b. Convert \(\frac{9}{25}\) to decimal

Divide the numerator (9) by the denominator (25): \(9 \div 25 = 0.36\). Since this is already a terminating decimal, there is no need to round. So, \(\frac{9}{25} = 0.36\).

c. Convert \(\frac{5}{24}\) to decimal

Divide the numerator (5) by the denominator (24): \(5 \div 24 = 0.2083333...\). As this is a repeating decimal, round to the thousandths place, yielding \(\frac{5}{24} \approx 0.208\).

d. Convert \(\frac{1}{8}\) to decimal

Divide the numerator (1) by the denominator (8): \(1 \div 8 = 0.125\). Since this is already a terminating decimal, there is no need to round. So, \(\frac{1}{8} = 0.125\).

e. Convert \(\frac{3}{20}\) to decimal

Divide the numerator (3) by the denominator (20): \(3 \div 20 = 0.15\). Since this is already a terminating decimal, there is no need to round. So, \(\frac{3}{20} = 0.15\).

f. Convert \(2 \frac{5}{6}\) to decimal

First, let's convert the mixed number to an improper fraction: \(2 \frac{5}{6} = \frac{12+5}{6} = \frac{17}{6}\). Next, divide the numerator (17) by the denominator (6): \(17 \div 6 = 2.8333333...\). As this is a repeating decimal, round to the thousandths place, yielding \(2 \frac{5}{6} \approx 2.833\).

g. Convert \(\frac{3}{7}\) to decimal

Divide the numerator (3) by the denominator (7): \(3 \div 7 = 0.428571...\). As this is a repeating decimal, round to the thousandths place, yielding \(\frac{3}{7} \approx 0.429\).

h. Convert \(\frac{11}{8}\) to decimal

Divide the numerator (11) by the denominator (8): \(11 \div 8 = 1.375\). Since this is already a terminating decimal, there is no need to round. So, \(\frac{11}{8} = 1.375\).