Multiplying Decimals
Decimals practice
Multiply decimals by whole numbers or decimals. Exact products can need up to four decimal places.
Decimals practice
Multiply decimals by whole numbers or decimals. Exact products can need up to four decimal places.
Multiply a decimal by a whole number or another decimal, and type the exact product.
The factors have up to two decimal places. Some products need three or four decimal places. A zero at the end does not change a value, so 0.42 and 0.420 are the same answer.
Typical level: Grade 5In the U.S. Common Core, Grade 5 includes multiplying decimals to hundredths. This practice uses factors through hundredths and keeps products exact, sometimes with three or four decimal places. Curriculum timing varies.
One tenth × one tenth = one hundredth. So 0.6 × 0.4 is 6 tenths × 4 tenths:
The product has two decimal places because tenths times tenths make hundredths. Multiplication can need more decimal places than either factor.
Both factors are less than 1, so the product is smaller than either factor.
For help naming tenths and hundredths, try Decimal Place Value.
Place value explains the written procedure, too. In 1.2 × 0.35, 1.2 represents 12 tenths and 0.35 represents 35 hundredths. A tenth × a hundredth is a thousandth, so 420 represents 420 thousandths.
Example: 1.2 × 0.35
Do not line up decimal points when multiplying. Addition and subtraction align matching place values. For multiplication, multiply the digits as whole-number equivalents, then use the place values of both factors to place the decimal.
A whole-number factor contributes zero decimal places. Count only the decimal places in the other factor.
7 × 8 = 56
2 + 2 = 4 decimal places
0.07 × 0.08 = 0.0056
The product needs four decimal places. The zeros after the decimal point hold the empty tenths and hundredths places. The zero before the decimal point shows there are no whole units.