Multiply Decimals - Arithmetic Step by Step

Multiply 2.4 × 0.13 by ignoring the decimal points and multiplying the integers 24 × 13 = 312, then counting the total decimal places (1 + 2 = 3) and inserting the decimal point three places from the right: 312 → 0.312.

decimal-multiplication Multiply as if both numbers are integers (ignore the decimal points). Count the total number of decimal places in both factors. In the product, count that many digits from the right and insert the decimal point there.

Example

Multiply 2.4 by 0.13, then place the decimal point.

highlighted = computed this step

Step 1 — Set up

Start with the decimal multiplication.

2.4\times 0.13

Step 2 — Partial product

Ones digit 3: 4 x 3 = 12, write 2, carry 1; partial 72.

\begin{array}{rrrr}\phantom{x}&\phantom{x}&\hl{1}&\phantom{x}\\\phantom{x}&\phantom{x}&2&4\\\times&\phantom{x}&1&3\\\hline\\\phantom{x}&\phantom{x}&\hl{7}&\hl{2}\\\phantom{x}&\square&\square&\square\\\hline\\\phantom{x}&\square&\square&\square\end{array}

Step 3 — Partial product

Tens digit 1: 24 x 1 = 24, shift left to 240.

\begin{array}{rrrr}\phantom{x}&\phantom{x}&2&4\\\times&\phantom{x}&1&3\\\hline\\\phantom{x}&\phantom{x}&7&2\\\phantom{x}&\hl{2}&\hl{4}&\hl{0}\\\hline\\\phantom{x}&\square&\square&\square\end{array}

Step 4 — Whole-number product

Add partials to get 312.

\begin{array}{rrrr}\phantom{x}&\phantom{x}&2&4\\\times&\phantom{x}&1&3\\\hline\\\phantom{x}&\phantom{x}&7&2\\\phantom{x}&2&4&0\\\hline\\\phantom{x}&\hl{3}&\hl{1}&\hl{2}\end{array}

Step 5 — Count decimal places

Count decimal places: 1 + 2 = 3.

1+2=\hl{3}

Step 6 — Place decimal

Move the decimal 3 places: 312 becomes 0.312.

312\rightarrow \hl{0.312}

Step 7 — Result

Read the result: 0.312.

2.4\times 0.13=0.312