Multiply decimals by decimals

Multiplication of decimals is understood as scaling quantities by factors that may be less than, equal to, or greater than one, with place value determining the size and position of the product; decimals can be interpreted as fractions with denominators of powers of ten or represented by rectangular areas. The written method connects whole-number multiplication to the total number of decimal places, and estimation helps detect misplaced decimal points and unreasonable results; this scope excludes repeating decimals and more advanced generalizations of decimal multiplication.

Detailed Explanation: Multiply decimals by decimals

To multiply decimals, first multiply as if they were whole numbers. Then place the decimal point by counting the total number of decimal places in the factors.

Example: Find $(2.4 \times 1.3)$

Estimate the answer.
Since $(2.4)$ is about $2$ and $(1.3)$ is about $1$ , the answer should be around $2$ or $3$ .
Ignore the decimal points and multiply.
Multiply $(24 \times 13)$ :

24 \times 13 = 312

Count the decimal places.
- $(2.4)$ has $1$ decimal place.
- $(1.3)$ has $1$ decimal place.
There are $(1+1=2)$ decimal places altogether.
Place the decimal point in the product.
Starting from the right in $(312)$ , move the decimal point $2$ places left:

312 \longrightarrow 3.12

Therefore,

\boxed{2.4 \times 1.3 = 3.12}

The answer makes sense because multiplying $(2.4)$ by $(1.3)$ makes it larger than $(2.4)$ , but not by a huge amount.

Learn by doing: Multiply decimals by decimals

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Multiplication - Decimal Tenths

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