Math Background

Place Value and Money: Overview

Our number system is a place-value system. This means that each place in a number is assigned a value. The value of each place in the base-ten system we use is ten times the value of the place to its right.

place-value chart

Your students learned place value to hundred thousands in Grade 3. See Place Value to 999,999. This year, they will apply place-value skills to hundred millions. Notice that the places are in groups of three. Each group is called a period. Periods are separated by commas.

place-value chart

The number in the place-value chart above can be written different ways.

  • The standard form is 745,309,281.
  • The expanded form is
    700,000,000 + 40,000,000 + 5,000,000 + 300,000 + 9,000 + 200 + 80 + 1.
  • The short word form is 745 million, 309 thousand, 281.
  • The word form is seven hundred forty-five million, three hundred nine thousand, two hundred eighty-one.

Use the Introducing the Concept lesson Comparing and Ordering Greater Numbers on this Web site to present place value through hundred millions to your students. Then proceed to the Developing the Concept lesson to explore comparing and ordering greater numbers on a place-value chart. With a solid foundation in place value, students will easily make the transition to comparing numbers without a place-value chart. Look at the example below.

Compare 3,924,761 and 3,915,804.

Line up the digits and start with the greatest place value.

Compare 3,924,761 and 3,915,804.

3,924,761 > 3,915,804

Students will also rely upon their place-value skills when they round greater numbers.

To round 28,734,115 to the nearest million, find the place you want to round to and look at the digit to its right.

28,734,115

7 > 5, so change 8 to 9 and write zeros to the right.

28,734,115 rounds to 29,000,000.

Remember:

  • When the digit to the right of the digit in the place you are rounding to is less than 5, do not change the digit in the place you are rounding to. Just write zeros to the right of it.

    5,316,220 rounded to the nearest hundred thousand is 5,300,000.

  • When the digit to the right of the digit in the place you are rounding to is 5 or greater than 5, increase the digit in the place you are rounding to. Then write zeros to the right of it.

    375,521,008 rounded to the nearest ten million is 380,000,000.

    The second half of the chapter focuses on money. You can use the Introducing the Concept part of the lesson Comparing Money Amounts on this Web site to review counting bills and coins; then you can move on to comparing amounts of money in the Developing the Concept part.

  • Count on to find the total value of the money.
One five-dollar bill, two one-dollar bills, one quarter, two nickels and one penny equal seven dollars and thirty-six cents.

The total value of the money is $7.36.

  • Is $7.36 greater than, less than, or equal to $7.50?

    $7.36 is less than $7.50.

    The second lesson covers making change.

  • Count on from the cost of the item to the amount paid.
A one-dollar bill, one quarter, and two pennies equals change for eight dollars and seventy three cents from ten dollars

The change is $1.27.

Give your students many opportunities to make change. See suggestions in the Tips and Tricks section of this topic.


Houghton Mifflin Math Grade 4