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Accepted Answer

### Set A Solutions:
#### 1. $0.1 \times 0.3$
# Explanation:
## Step1: Multiply the numbers as whole numbers.
$1 \times 3 = 3$
## Step2: Count the total decimal places.
$0.1$ has 1 decimal place, $0.3$ has 1 decimal place, so total is $1 + 1 = 2$ decimal places.
## Step3: Place the decimal in the product.
$3$ with 2 decimal places is $0.03$.
# Answer: $0.03$

#### 2. $0.1 \times 0.6$
# Explanation:
## Step1: Multiply as whole numbers.
$1 \times 6 = 6$
## Step2: Count decimal places.
$0.1$ (1) + $0.6$ (1) = 2 decimal places.
## Step3: Place decimal.
$6$ with 2 decimal places is $0.06$.
# Answer: $0.06$

#### 3. $0.2 \times 0.3$
# Explanation:
## Step1: Whole number multiplication.
$2 \times 3 = 6$
## Step2: Decimal places.
$0.2$ (1) + $0.3$ (1) = 2.
## Step3: Place decimal.
$6$ with 2 decimal places is $0.06$.
# Answer: $0.06$

#### 4. $0.2 \times 0.6$
# Explanation:
## Step1: Whole number multiply.
$2 \times 6 = 12$
## Step2: Decimal places.
$0.2$ (1) + $0.6$ (1) = 2.
## Step3: Place decimal.
$12$ with 2 decimal places is $0.12$.
# Answer: $0.12$

#### 5. $0.4 \times 0.3$
# Explanation:
## Step1: Whole number multiply.
$4 \times 3 = 12$
## Step2: Decimal places.
$0.4$ (1) + $0.3$ (1) = 2.
## Step3: Place decimal.
$12$ with 2 decimal places is $0.12$.
# Answer: $0.12$

#### 6. $0.4 \times 0.6$
# Explanation:
## Step1: Whole number multiply.
$4 \times 6 = 24$
## Step2: Decimal places.
$0.4$ (1) + $0.6$ (1) = 2.
## Step3: Place decimal.
$24$ with 2 decimal places is $0.24$.
# Answer: $0.24$

#### 7. $0.8 \times 0.3$
# Explanation:
## Step1: Whole number multiply.
$8 \times 3 = 24$
## Step2: Decimal places.
$0.8$ (1) + $0.3$ (1) = 2.
## Step3: Place decimal.
$24$ with 2 decimal places is $0.24$.
# Answer: $0.24$

#### 8. $0.8 \times 0.6$
# Explanation:
## Step1: Whole number multiply.
$8 \times 6 = 48$
## Step2: Decimal places.
$0.8$ (1) + $0.6$ (1) = 2.
## Step3: Place decimal.
$48$ with 2 decimal places is $0.48$.
# Answer: $0.48$

#### 9. $1.6 \times 0.3$
# Explanation:
## Step1: Whole number multiply.
$16 \times 3 = 48$
## Step2: Decimal places.
$1.6$ (1) + $0.3$ (1) = 2.
## Step3: Place decimal.
$48$ with 2 decimal places is $0.48$.
# Answer: $0.48$

#### 10. $1.6 \times 0.6$
# Explanation:
## Step1: Whole number multiply.
$16 \times 6 = 96$
## Step2: Decimal places.
$1.6$ (1) + $0.6$ (1) = 2.
## Step3: Place decimal.
$96$ with 2 decimal places is $0.96$.
# Answer: $0.96$

#### 11. $3.2 \times 0.3$
# Explanation:
## Step1: Whole number multiply.
$32 \times 3 = 96$
## Step2: Decimal places.
$3.2$ (1) + $0.3$ (1) = 2.
## Step3: Place decimal.
$96$ with 2 decimal places is $0.96$.
# Answer: $0.96$

#### 12. $3.2 \times 0.6$
# Explanation:
## Step1: Whole number multiply.
$32 \times 6 = 192$
## Step2: Decimal places.
$3.2$ (1) + $0.6$ (1) = 2.
## Step3: Place decimal.
$192$ with 2 decimal places is $1.92$.
# Answer: $1.92$

### Set B Solutions:
#### 1. $34.5 \times 5$
# Explanation:
## Step1: Multiply as whole numbers.
$345 \times 5 = 1725$
## Step2: Count decimal places in the first number.
$34.5$ has 1 decimal place.
## Step3: Place decimal.
$1725$ with 1 decimal place is $172.5$.
# Answer: $172.5$

#### 2. $34.5 \times 0.5$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$34.5$ (1) + $0.5$ (1) = 2.
## Step3: Place decimal.
$1725$ with 2 decimal places is $17.25$.
# Answer: $17.25$

#### 3. $34.5 \times 0.05$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$34.5$ (1) + $0.05$ (2) = 3.
## Step3: Place decimal.
$1725$ with 3 decimal places is $1.725$.
# Answer: $1.725$

#### 4. $34.5 \times 0.005$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$34.5$ (1) + $0.005$ (3) = 4.
## Step3: Place decimal.
$1725$ with 4 decimal places (add a leading zero) is $0.1725$.
# Answer: $0.1725$

#### 5. $3.45 \times 5$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$3.45$ has 2 decimal places.
## Step3: Place decimal.
$1725$ with 2 decimal places is $17.25$.
# Answer: $17.25$

#### 6. $3.45 \times 0.5$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$3.45$ (2) + $0.5$ (1) = 3.
## Step3: Place decimal.
$1725$ with 3 decimal places is $1.725$.
# Answer: $1.725$

#### 7. $3.45 \times 0.05$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$3.45$ (2) + $0.05$ (2) = 4.
## Step3: Place decimal.
$1725$ with 4 decimal places (add a leading zero) is $0.1725$.
# Answer: $0.1725$

#### 8. $3.45 \times 0.005$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$3.45$ (2) + $0.005$ (3) = 5.
## Step3: Place decimal.
$1725$ with 5 decimal places (add two leading zeros) is $0.01725$.
# Answer: $0.01725$

#### 9. $0.345 \times 5$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$0.345$ has 3 decimal places.
## Step3: Place decimal.
$1725$ with 3 decimal places is $1.725$.
# Answer: $1.725$

#### 10. $0.345 \times 0.5$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$0.345$ (3) + $0.5$ (1) = 4.
## Step3: Place decimal.
$1725$ with 4 decimal places (add a leading zero) is $0.1725$.
# Answer: $0.1725$

#### 11. $0.345 \times 0.05$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$0.345$ (3) + $0.05$ (2) = 5.
## Step3: Place decimal.
$1725$ with 5 decimal places (add two leading zeros) is $0.01725$.
# Answer: $0.01725$

#### 12. $0.345 \times 0.005$
# Explanation:
## Step1: Whole number multiply.
$345 \times 5 = 1725$
## Step2: Decimal places.
$0.345$ (3) + $0.005$ (3) = 6.
## Step3: Place decimal.
$1725$ with 6 decimal places (add three leading zeros) is $0.001725$.
# Answer: $0.001725$

### Pattern Description (for Set B as an example):
In Set B, when the multiplier (the second number) is divided by 10 (e.g., from $5$ to $0.5$ to $0.05$ to $0.005$), the product is also divided by 10. Also, when the multiplicand (the first number) is divided by 10 (e.g., from $34.5$ to $3.45$ to $0.345$), the product is also divided by 10, assuming the multiplier remains in a corresponding scale. For example, $34.5 \times 5 = 172.5$, $3.45 \times 5 = 17.25$ (divided by 10), $0.345 \times 5 = 1.725$ (divided by 10 again). Similarly, $34.5 \times 0.5 = 17.25$, $3.45 \times 0.5 = 1.725$ (divided by 10), etc. This shows the effect of decimal places (or place value) on the product when multiplying decimals.

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QUESTION IMAGE

Question

Explanation:

Set A Solutions:

1. \(0.1 \times 0.3\)

Step1: Multiply the numbers as whole numbers.

Step2: Count the total decimal places.

Step3: Place the decimal in the product.

Step1: Multiply as whole numbers.

Step2: Count decimal places.

Step3: Place decimal.

Step1: Whole number multiplication.

Step2: Decimal places.

Step3: Place decimal.

Answer:

2. \(0.1 \times 0.6\)