Multiplying and Dividing Decimals

Multiplying Decimals

Multiplying decimals is similar to multiplying whole numbers. Standard algorithms tell us to "ignore" the decimal point while doing the calculations and then determine where the decimal point should be in the product.

Before performing the multiplication, the product of 5.6 x 3.2 can be roughly estimated as being a bit larger than 5 x 3 = 15.

The original estimate was for the product to be a bit larger than 15, so the answer given is reasonable. If the decimal point had been misplaced as 1.782 or 178.2, these product should be recognized as not being reasonable.

Any method of multiplication that can be used with whole numbers can be used when multiplying decimal numbers, since the two are identical except for counting decimal places in the factors and applying that to the product. Below is an example using lattice multiplication.

One thing stands out when multiplying by a decimal number between 0 and 1: multiplying by such a number leads to a product that is less than the original number.

If 7 x 3 can be thought of as "three sevens" or seven added together three times, then 7 x 0.5 can be thought of as "half of seven" and 7 x 0.25 as "one fourth of seven."

The video below shows how to count the digits to the right of the decimal point to correctly place the decimal point when solving the following multiplication problems.

Dividing Decimals

Like with multiplication, dividing with decimals is quite similar to dividing whole numbers. When using the standard algorithm, much care must be taken when placing the digits in the quotient, since the decimal point will be placed in the correct spot after completing the division steps.

When the divisor is a decimal number, there is an additional consideration. Before carrying out the division, the divisor is multiplied by a power of ten (by 10 or 100 or 1,000) so that becomes a whole number. Then, whatever the divisor is multiplied by, the dividend is also multiplied by that power of ten. Multiplying both the divisor and dividend by the same number creates a problem equivalent to the original one.

The practical way of looking at this is to move the decimal point of both the divisor and dividend the same number of places to the right.