Math Background

Multiplying and Dividing Decimals: When Students Ask

  • How can I check my answer when I multiply with decimals?
    The first thing students should do is estimate to see if the product is reasonable.
    multiplication problem

    The answer should be about 3.

    multiplication problem

    After students multiply and place the decimal point, they can switch the order of the factors and multiply again. The commutative property of multiplication states that the products are the same.

    2.9 x 1.06 = 1.06 x 2.9

    multiplication problem
  • What's an exponent and when do I use one?
    An exponent is a number raised to a power that tells how many times a factor, or base, is repeated in a product. For 4² the exponent, 2, shows the number of times the base, 4, is used as a factor. So 4² = 4 x 4 = 16.

    The Milky Way galaxy could contain an estimated one hundred billion stars. Which number is simpler to write—100,000,000,000 or 1011? 1011 is a quick way to write 100 billion. The exponent, 11, tells us how many times the base, 10, is used as a factor:

    1011 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
    54 = 5 x 5 x 5 x 5 = 625
    23 = 2 x 2 x 2 = 8
    75 = 7 x 7 x 7 x 7 x 7 = 16,807

    Very large powers of ten are frequently written using exponents. In this century the population of Earth could reach 10,000,000,000 or 1010.

  • Where do I place the decimal point when I divide?
    The rule for students to remember when dividing by a whole number is to place the decimal point in the quotient directly above the decimal point in the dividend.
    multiplication problem

    This rule also applies when dividing a decimal by a decimal but the decimal point in the dividend must be moved first.
    Dance tickets cost $0.75, and $85.50 was collected at the door. How many tickets were sold?

    multiplication problem

    114 tickets were sold.

  • Why are decimals so important?
    All of our dealings with our money system involve decimals, and it is important to be skilled in all operations involving decimals.
    If you start your first job as a teenager making $6.25 an hour, and you work 14 hours the first week, your paycheck should show your wages to be $87.50. If the decimal point was accidentally moved one place to the left, your check would show only $8.75 in earnings.

Houghton Mifflin Math Grade 5