Question: 9 Division by Decimals In division, the divisor must be a whole number. To convert a decimal divisor to a whole number, multiply the divisor and the dividend by a multiple of ten. Then divide as usual. Example: 4.9 ÷ 0.7 (4.9 x 10) ÷ (0.7 x 10) 49 ÷ 7 = 7 Example: 8.505 100 0.05 x 100 = 850.5 5)850.5 5 35 35 005 5 0 The divisor (0.7) has one decimal place. To change the divisor to a whole number, multiply the divisor and the dividend by 10. Divide as usual. The divisor (0.05) has two decimal places. To change the divisor to a whole number, multiply the divisor and the dividend by 100. Divide as usual. Place the decimal point for the quotient (170.1) directly above the decimal point in the dividend (850.5) Divide: 1) 574.0 ÷ 0.7 2) 0.4)6.988 3) 0.0144 1.2 4) 35.1 ÷ 2.7 5) 2.4)77.04 6) 0.132 0.011 7) 82.8 ÷ 0.03 8) 0.41)205 9) 0.6832 0.004

1. **Problem:** Divide $574.0$ by $0.7$. 2. **Rule:** To divide by a decimal, multiply both dividend and divisor by $10^{n}$ where $n$ is the number of decimal places in the divisor. 3. Here, divisor $0.7$ has $1$ decimal place, so multiply both by $10$: $$574.0 \times 10 = 5740$$ $$0.7 \times 10 = 7$$ 4. Now divide $5740 \div 7$: $$7 \times 820 = 5740$$ 5. So, $574.0 \div 0.7 = 820$. --- 1. **Problem:** Divide $6.988$ by $0.4$. 2. Divisor $0.4$ has $1$ decimal place, multiply both by $10$: $$6.988 \times 10 = 69.88$$ $$0.4 \times 10 = 4$$ 3. Divide $69.88 \div 4$: $$4 \times 17.47 = 69.88$$ 4. So, $6.988 \div 0.4 = 17.47$. --- 1. **Problem:** Divide $0.0144$ by $1.2$. 2. Divisor $1.2$ has $1$ decimal place, multiply both by $10$: $$0.0144 \times 10 = 0.144$$ $$1.2 \times 10 = 12$$ 3. Divide $0.144 \div 12$: $$12 \times 0.012 = 0.144$$ 4. So, $0.0144 \div 1.2 = 0.012$. --- 1. **Problem:** Divide $35.1$ by $2.7$. 2. Divisor $2.7$ has $1$ decimal place, multiply both by $10$: $$35.1 \times 10 = 351$$ $$2.7 \times 10 = 27$$ 3. Divide $351 \div 27$: $$27 \times 13 = 351$$ 4. So, $35.1 \div 2.7 = 13$. --- 1. **Problem:** Divide $77.04$ by $2.4$. 2. Divisor $2.4$ has $1$ decimal place, multiply both by $10$: $$77.04 \times 10 = 770.4$$ $$2.4 \times 10 = 24$$ 3. Divide $770.4 \div 24$: $$24 \times 32.1 = 770.4$$ 4. So, $77.04 \div 2.4 = 32.1$. --- 1. **Problem:** Divide $0.132$ by $0.011$. 2. Divisor $0.011$ has $3$ decimal places, multiply both by $1000$: $$0.132 \times 1000 = 132$$ $$0.011 \times 1000 = 11$$ 3. Divide $132 \div 11$: $$11 \times 12 = 132$$ 4. So, $0.132 \div 0.011 = 12$. --- 1. **Problem:** Divide $82.8$ by $0.03$. 2. Divisor $0.03$ has $2$ decimal places, multiply both by $100$: $$82.8 \times 100 = 8280$$ $$0.03 \times 100 = 3$$ 3. Divide $8280 \div 3$: $$3 \times 2760 = 8280$$ 4. So, $82.8 \div 0.03 = 2760$. --- 1. **Problem:** Divide $205$ by $0.41$. 2. Divisor $0.41$ has $2$ decimal places, multiply both by $100$: $$205 \times 100 = 20500$$ $$0.41 \times 100 = 41$$ 3. Divide $20500 \div 41$: $$41 \times 500 = 20500$$ 4. So, $205 \div 0.41 = 500$. --- 1. **Problem:** Divide $0.6832$ by $0.004$. 2. Divisor $0.004$ has $3$ decimal places, multiply both by $1000$: $$0.6832 \times 1000 = 683.2$$ $$0.004 \times 1000 = 4$$ 3. Divide $683.2 \div 4$: $$4 \times 170.8 = 683.2$$ 4. So, $0.6832 \div 0.004 = 170.8$.