Method 1: The Fraction Shortcut

One way to understand decimal multiplication is to convert the decimals into fractions first. Since decimals are just another way of writing tenths, hundredths, or thousandths, we can use what we know about fractions to solve the problem.

Example: $0.2 \times 0.3$

1. Convert to fractions: $0.2$ becomes $\frac{2}{10}$ and $0.3$ becomes $\frac{3}{10}$.

2. Multiply across: $\frac{2}{10} \times \frac{3}{10} = \frac{6}{100}$.

3. Convert back to decimal: $\frac{6}{100}$ is written as 0.06.

Method 2: The “Count the Places” Method

This is the most popular method because it allows you to treat the numbers like regular integers until the very last second.

The Steps:

1. Ignore the decimals and multiply the numbers as if they were whole numbers.

2. Count the total number of digits to the right of the decimal point in both original numbers.

3. Place the decimal point in your answer by counting from right to left.

See it in action:

Case A: Small Decimals

• Problem: $0.2 \times 0.3$

• Step 1: Multiply $2 \times 3 = 6$.

• Step 2: Count decimal places. $0.2$ has 1 place, and $0.3$ has 1 place. Total = 2 places.

• Step 3: Starting from the right of 6, move the decimal 2 places left.

• Result: 0.06

Case B: Larger Numbers ($11.2 \times 0.15$)

• Step 1: Multiply $112 \times 15$. We get 1680.

• Step 2: Count decimal places. $11.2$ (1 place) + $0.15$ (2 places) = 3 total places.

• Step 3: Move the decimal 3 places to the left in 1680.

• Result: 1.680

Case C: Decimal by Whole Number ($2.71 \times 7$)

• Step 1: Multiply $271 \times 7$. We get 1897.

• Step 2: Count decimal places. $2.71$ (2 places) + $7$ (0 places) = 2 total places.

• Step 3: Move the decimal 2 places to the left in 1897.

• Result: 18.97

Taking Decimals to the Power of 3

When you see a problem like $(1.2)^3$, it simply means you need to multiply $1.2$ by itself three times:

Step 1: Multiply as Whole Numbers

First, ignore the decimals and treat the problem as $12 \times 12 \times 12$:

• $12 \times 12 = 144$

• $144 \times 12 = 1728$

Step 2: Count the Decimal Places

Now, look back at the original problem ($1.2 \times 1.2 \times 1.2$) and count how many digits are to the right of the decimal point:

• 1.2 has 1 decimal place.

• Since we have three of them, we add them together: $1 + 1 + 1 =$ 3 total decimal places.

Step 3: Place the Decimal Point

Start at the right of your whole-number answer (1728) and move the decimal point 3 places to the left:

Final Answer: $(1.2)^3 = 1.728$