Express the following decimals as proper fractions. Give your answers in lowest terms. a) 0.41 b) 0.6 c) 0.36 d) 0.72 e) 0.125

Since 41 is a prime number and 100 is not divisible by 41, the fraction is already in its lowest terms.

$$\boxed{\frac{41}{100}}$$

b) 0.6

$$\frac{6 \div 2}{10 \div 2} = \frac{3}{5}$$ $$\boxed{\frac{3}{5}}$$

c) 0.36

$$\frac{36 \div 4}{100 \div 4} = \frac{9}{25}$$ $$\boxed{\frac{9}{25}}$$

d) 0.72

$$\frac{72 \div 4}{100 \div 4} = \frac{18}{25}$$ $$\boxed{\frac{18}{25}}$$

e) 0.125

$$\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}$$ $$\boxed{\frac{1}{8}}$$

2. Convert the following to improper fractions.

a) 8.4

Multiply the whole number by the denominator and add the numerator.

$$\frac{(8 \times 5) + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5}$$ $$\boxed{\frac{42}{5}}$$

b) 2.64

$$\frac{(2 \times 25) + 16}{25} = \frac{50 + 16}{25} = \frac{66}{25}$$ $$\boxed{\frac{66}{25}}$$

c) 7.24

$$\frac{(7 \times 25) + 6}{25} = \frac{175 + 6}{25} = \frac{181}{25}$$ $$\boxed{\frac{181}{25}}$$

d) 6.25

$$\frac{(6 \times 4) + 1}{4} = \frac{24 + 1}{4} = \frac{25}{4}$$ $$\boxed{\frac{25}{4}}$$

e) 3.125

$$\frac{(3 \times 8) + 1}{8} = \frac{24 + 1}{8} = \frac{25}{8}$$ $$\boxed{\frac{25}{8}}$$

3. Express the following decimals as mixed numbers.

a) 3.248

$$\boxed{3 \frac{31}{125}}$$

b) 6.45

$$\boxed{6 \frac{9}{20}}$$

c) 9.05

$$\boxed{9 \frac{1}{20}}$$

d) $