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.
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 × 0.13 2.4\times 0.13 2.4 × 0.13
Step 2 — Partial product
Ones digit 3: 4 x 3 = 12, write 2, carry 1; partial 72.
x x 1 x x x 2 4 × x 1 3 x x 7 2 x □ □ □ x □ □ □ \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} x x × x x x x x x x □ □ 1 2 1 7 □ □ x 4 3 2 □ □
Step 3 — Partial product
Tens digit 1: 24 x 1 = 24, shift left to 240.
x x 2 4 × x 1 3 x x 7 2 x 2 4 0 x □ □ □ \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} x × x x x x x x 2 □ 2 1 7 4 □ 4 3 2 0 □
Step 4 — Whole-number product
Add partials to get 312.
x x 2 4 × x 1 3 x x 7 2 x 2 4 0 x 3 1 2 \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} x × x x x x x x 2 3 2 1 7 4 1 4 3 2 0 2
Step 5 — Count decimal places
Count decimal places: 1 + 2 = 3.
2.4 has 1 decimal place and 0.13 has 2 decimal places: total 3 2.4: 1 place 0.13: 2 places total: 3 3 1 2 whole-number product 312
Step 6 — Place decimal
Move the decimal 3 places: 312 becomes 0.312.
312 → 0.312 312\rightarrow \hl{0.312} 312 → 0.312 Move the decimal 3 places from the right of 312 2.4: 1 place 0.13: 2 places total: 3 0 3 1 2 . count 3 digits
Step 7 — Result
Read the result: 0.312.
2.4 × 0.13 = 0.312 2.4\times 0.13=0.312 2.4 × 0.13 = 0.312 312 becomes 0.312 2.4: 1 place 0.13: 2 places total: 3 0 3 1 2 . count 3 digits
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.