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Decimals Adding and subtracting decimals Decimal number lineHere you will learn about place value, including the names and values of the different positions.
Students will first learn about place value as part of their work with numbers and operations in base ten in elementary school.
Place value is the value of each digit within a number.
A number is made up of digits. For example, the number 54 has two digits, 5 and 4. The value of each digit can help us understand the size of the number.
To determine the value of a digit within a number you use a place value chart.
For example, for 54, the 5 is in the tens column and the 4 is in the ones column.
This means that the number 54 is equivalent to 5 tens and 4 ones.
5 tens is the same as 5\times{10}=50 and 4 ones is the same as 4\times{1}=4.
Adding 50+4 gives us the number 54.
Here are the digits to the left of the decimal point.
Let’s write the number nine million, four hundred and fifty thousand, three hundred and eighty two in the place value chart:
Notice you use a comma after the millions digit (9) and the thousands digit (0).
The comma is used to the left of the decimal point to separate 3 digits at a time.
If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the thousands position, the number would read 945,382 which is a different number from the number above.
The place value chart above shows positions up to the millions. However, you can use place value to represent very large numbers.
Place Value | Ordinary Number | Power of \bf{10} |
---|---|---|
Thousands | 1,000 | 10^3 |
Millions | 1,000,000 | 10^6 |
Billions | 1,000,000,000 | 10^9 |
Trillions | 1,000,000,000,000 | 10^{12} |
Quadrillions | 1,000,000,000,000,000 | 10^{15} |
Googol | 10,000,000,000,000,000,000,000,000,
| 10^{100} |
Here are the digits to the right of the decimal point.
Let’s write the number two and thirty four thousandths in the place value chart:
There is a period after the ones digit (2). The period tells us that the next part of the number is a decimal or less than 1.
If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the tenths position, the number would read 2.34 which is a different number from the number above.
The place value chart above shows numbers down to the thousandths. However, you can use place value to represent very small numbers.
Place Value | Ordinary Number | Power of \bf{10} |
---|---|---|
Thousandths | 0.001 | 10^{-3} |
Millionths | 0.000001 | 10^{-6} |
Billionths | 0.000000001 | 10^{-9} |
Trillionths | 0.000000000001 | 10^{-12} |
How does this relate to 2nd grade math, 4th grade math and 5th grade math?
In order to write the value of a digit in a number:
Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with this assessment
DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with this assessment
DOWNLOAD FREEWhat is the value of the digit 3 in 4,163?
2Use the place value chart to find the position.
The 3 is in the ones column.
3Write the value of the digit.
The value of the digit 3 in the number 4,163 is 3 ones, or 3.
What is the value of the digit 4 in 385,431?
Find the digit within the number.
Use the place value chart to find the position.
The 4 is in the hundreds column.
Write the value of the digit.
The value of the digit 4 in the number 385,431 is four hundreds, or 400.
What is the value of the digit 2 in 1,025,634?
Find the digit within the number.
Use the place value chart to find the position.
The 2 is in the ten thousands column.
Write the value of the digit.
The value of the digit 2 in the number 1,025,634 is twenty thousands, or 20,000.
What is the value of the digit 2 in 3.264?
Find the digit within the number.
Use the place value chart to find the position.
The 2 is in the tenths column.
Write the value of the digit.
The value of the digit 2 in the number 3.264 is two tenths, or 0.2.
What is the value of the digit 7 in 0.078?
Find the digit within the number.
Recall the place value of that column.
The 7 is in the hundredths column.
Write the value of the digit.
The value of the digit 7 in the number 0.078 is seven hundredths, or 0.07.
What is the value of the digit 4 in 10.054?
Locate the digit within the number.
Use the place value chart to find the position.
The 4 is in the thousandths column.
Write the value of the digit.
The value of the digit 4 in the number 10.054 is four thousandths, or 0.004.
1. What is the value of 2 in 475,321?
Two hundreds
The digit 2 is in the tens column, so the value is 2 tens or 20.
2. What is the value of 1 in 1,000,253?
One hundred thousand
The digit 1 is in the millions column, so the value is 1 million or 1,000,000.
3. What is the value of 3 in 483,201?
Ten thousand
The digit 3 is in the thousands column, so the value is 3 thousands or 3,000.
4. What is the value of 7 in 6.072?
Seven hundreds
Seven tenths
Seven tens
Seven hundredths
The digit 7 is in the hundredths column, so the value is 7 hundredths or 0.07.
5. What is the value of 8 in 0.008?
Eight thousandths
Eight tenths
Eight thousands
Eight ones
The digit 8 is in the thousandths column, so the value is 8 thousandths or 0.008.
6. What is the value of 4 in 4.825?
Four thousandths
0.4
The digit 4 is in the ones column, so the value is 4 ones or 4.
Our number system is called Base Ten, because ten is the value used to create the place value groupings. That is why all of the place value positions (like the tens place or hundreds place) are multiples of 10. This is also why younger students practice skip counting by tens, which ultimately helps them recognize patterns in our number system.
Place value helps you understand the size of a number and gives meaning to the digits in each position. An understanding of place value can help you when comparing numbers and ordering numbers and is also essential when operating with numbers.
Per the Common Core, in fifth grade students work with the tenths place, the hundredths place and the thousandths place. Sixth graders should extend this to smaller positions. It is also important to be mindful of standard expectations, as they may vary from state to state.
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