Place Values
The Whole Numbers
You might remember that counting numbers can also be called natural numbers. Let’s use this idea to define whole numbers.
whole numbers: are all natural numbers and zero. They are real numbers that do not include fractions, decimals, or negative numbers.
Let’s look at this number: 123,456,789
We have learned how to say this number with the counting or cardinal numbers:
One hundred twenty-three, four hundred fifty-six, seven hundred eighty-nine.
Okay, great!
The number, 123,456,789 has nine digits. Each digit is in a position. In math, we call the specific positions “place values”.
For example in the number 987, nine is in the hundreds place value or 900.
In the 9,341, nine is in the thousands place value or 9,000.
Both numbers are 9, but their place values are in different positions.
| hundred-millions | ten-millions | millions | hundred-thousands | ten-thousands | thousands | hundreds | tens | ones | |
| A.) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| B.) | |||||||||
| C.) |
Look at letter A.)
- The place value for one is hundred-millions.
- Number two is in the ten-millions place.
- The place value for three is millions.
- Number four is in the hundred-thousands place.
- The place value for five is ten-thousands.
- Number six is in the thousands place.
- The place value for seven is hundreds.
- Number eight is in the tens place.
- The place value for nine is ones.
Your Turn
| hundred-millions | ten-millions | millions | hundred-thousands | ten-thousands | thousands | hundreds | tens | ones | |
| B.) | 7 | 8 | 9 | 1 | 2 | 3 | 4 | 5 | 6 |
| hundred-millions | ten-millions | millions | hundred-thousands | ten-thousands | thousands | hundreds | tens | ones | |
| C.) | 2 | 4 | 6 | 8 | 9 | 7 | 5 | 3 | 1 |
The Decimal Point
Whole numbers are complete. There is no part of something with a whole number. A $10 bill means you have 10 whole dollars.
If you have $10.25, you have ten whole numbers and .25 of one dollar. This .25 means there is less than one whole dollar.
A decimal point occurs to the right of whole numbers.
| hundreds | tens | ones | decimal point | |||
| D.) | 1 | 0 | . | 2 | 5 |
The interesting thing about money is the decimals use the counting or cardinal numbers. We say, “Ten dollars and twenty-five cents.”
Video about saying amounts of money
Watch this 3:50 video Reading prices in English by Listening2English, September 29, 20222.
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Sometimes, zeros can follow the decimal point.
| hundreds | tens | ones | decimal point | |||
| E.) | 4 | 2 | . | 0 | 0 | |
| F.) | 1 | 9 | 9 | . | 0 | 0 |
Many times, the numbers after the decimal point are blank.
| hundreds | tens | ones | decimal point | |||
| G.) | 1 | 0 | . | |||
| H.) | 2 | 3 | 7 | . | ||
| I.) | 5 | . |
The decimal point is always understood to be to the right of the ones place.
The Decimal Fractions
Decimal fractions (sometimes just called “decimals”) are the numbers to the right of the decimal point. These numbers inform us about the part that is less than one whole number. They are some part of a whole.
The place values for decimal fractions use the ordinal numbers to identify the position. Notice that the place value names end in the suffix -ths.
| hundreds | tens | ones | decimal point | tenths | hundredths | thousandths | ten-thousandths | hundred-thousandths | |
| J.) | 2 | 4 | 3 | . | 7 | 5 | 1 | 6 | 9 |
Look at J.)
The seven is in the tenths place.
Number five is in the hundredths place.
The one is in the thousandths place.
Number six is in the ten-thousandths place.
The nine is in the hundred-thousandths place.
Your Turn
| hundreds | tens | ones | decimal point | tenths | hundredths | thousandths | ten-thousandths | hundred-thousandths | |
| K.) | 7 | 5 | 9 | . | 3 | 1 | 2 | 4 | 6 |
| hundreds | tens | ones | decimal point | tenths | hundredths | thousandths | ten-thousandths | hundred-thousandths | |
| L.) | 8 | 6 | 4 | . | 9 | 7 | 2 | 3 | 1 |
Download and print the decimal exercise worksheet to the right. It will help you understand how to say decimal numbers.
Many times, decimals measure:
- how long something is (length),
- how heavy something is (weight), and
- how far something is (distance).
It is important you know the names of the place values for both whole numbers and decimal fractions.
Summary:
- Identify place values for whole numbers
- Identify place values for decimal numbers
- Practice writing decimal numbers and mixed numbers
- Practice saying decimal numbers and mixed numbers
