Question

find each product. show your reasoning.
a. $(1.2) \cdot (0.11)$

b. $(0.34) \cdot (0.02)$

c. $120 \cdot (0.002)$

Explanation:

Part a: \((1.2) \cdot (0.11)\)

Step1: Multiply as integers

First, ignore the decimal points and multiply \(12\) and \(11\).
\(12 \times 11 = 132\)

Step2: Count decimal places

The number \(1.2\) has \(1\) decimal place, and \(0.11\) has \(2\) decimal places. So the total number of decimal places in the product is \(1 + 2 = 3\).

Step3: Place decimal in result

Starting from the right of \(132\), move the decimal point \(3\) places to the left.
\(132
ightarrow 0.132\) (we add a leading zero if necessary to have enough places)

Step1: Multiply as integers

Ignore the decimals and multiply \(34\) and \(2\).
\(34 \times 2 = 68\)

Step2: Count decimal places

\(0.34\) has \(2\) decimal places, \(0.02\) has \(2\) decimal places. Total decimal places: \(2 + 2 = 4\).

Step3: Place decimal in result

Move the decimal point \(4\) places left in \(68\). We need to add leading zeros: \(68
ightarrow 0.0068\) (since we need \(4\) decimal places, we have \(0.0068\) after moving the decimal)

Step1: Multiply as integers

Multiply \(120\) and \(2\) (ignoring the decimal in \(0.002\) for now).
\(120 \times 2 = 240\)

Step2: Count decimal places

\(0.002\) has \(3\) decimal places. So we need to move the decimal point \(3\) places left in the product.
\(240
ightarrow 0.240\) (which simplifies to \(0.24\) since the trailing zero after the decimal doesn't change the value)

Answer:

\(0.132\)

Part b: \((0.34) \cdot (0.02)\)