One Place to the Left
Moving one place to the left multiplies a place value by 10.
0.07 → 0.7
Free Math Guide
Decimal Place Value Explained
Learn how a digit's position determines its value, including ones, tenths, hundredths, thousandths, decimal fractions, and expanded form.
Decimal place value describes the value of each digit according to its position relative to the decimal point. Moving one place to the left makes a value ten times greater, while moving one place to the right makes it ten times smaller.
On This Page
- What decimal place value means
- Reading a decimal place-value chart
- The ones place
- The tenths place
- The hundredths place
- The thousandths place
- Finding the value of a digit
- Connecting decimals and fractions
- Writing decimals in expanded form
- Leading and trailing zeros
- Common decimal place-value mistakes
- Decimal place-value checklist
- Interactive practice
What Does Decimal Place Value Mean?
A digit does not always have the same value. Its value depends on where it appears in the number.
4
.
3
7
2
The Highlighted Digit
In 4.372, the digit 7 is in the hundredths place. Therefore, its value is 0.07, or seven hundredths.
One Place to the Right
Moving one place to the right divides a place value by 10.
0.7 → 0.07
The Digit and Its Value Are Not Always the Same
The highlighted digit may be 7, but its value could be 7, 0.7, 0.07, or 0.007 depending on its position.
Decimal Place-Value Chart
The decimal point separates whole-number places from fractional places.
Hundreds
100
Tens
10
Ones
1
Decimal Point
.
Tenths
1/10
Hundredths
1/100
Thousandths
1/1000
Example: Read 326.481
326.481
- The 3 is in the hundreds place and is worth 300.
- The 2 is in the tens place and is worth 20.
- The 6 is in the ones place and is worth 6.
- The 4 is in the tenths place and is worth 0.4.
- The 8 is in the hundredths place and is worth 0.08.
- The 1 is in the thousandths place and is worth 0.001.
There Is No “Oneths” Place
The first place to the right of the decimal point is tenths, not “oneths.”
The Ones Place
The ones place is immediately to the left of the decimal point. A digit in this position represents that many complete ones.
6
.
4
2
Digit
6
Highlighted digit = 6
Value
6
6 × 1 = 6
Ones Are Complete Units
In 6.42, the 6 represents six complete ones. It is not six tenths or six hundredths.
The Tenths Place
The first digit to the right of the decimal point is in the tenths place. Each tenth is one of ten equal parts of one whole.
3
.
8
5
Decimal Value
0.8
Eight tenths
Fraction Value
8
10
0.8 = 8/10
Example: Find the Value of 8 in 3.85
- Locate the decimal point.
- The 8 is the first digit to the right.
- Therefore, the 8 is in the tenths place.
- Its value is 0.8, or 8/10.
The digit 8 is worth eight tenths
Do Not Read 0.8 as Eight Hundredths
Because the 8 is in the first decimal place, it represents tenths.
The Hundredths Place
The second digit to the right of the decimal point is in the hundredths place. Each hundredth is one of one hundred equal parts of one whole.
4
.
3
7
2
Decimal Value
0.07
Seven hundredths
Fraction Value
7
100
0.07 = 7/100
Example: Find the Value of 7 in 4.372
- The first decimal digit, 3, is in the tenths place.
- The second decimal digit, 7, is in the hundredths place.
- Therefore, the 7 is worth 0.07.
The digit 7 is worth seven hundredths
The Zero Holds the Tenths Place
Writing 0.07 instead of 0.7 is important. The zero shows that there are no tenths before the seven hundredths.
The Thousandths Place
The third digit to the right of the decimal point is in the thousandths place. Each thousandth is one of one thousand equal parts of one whole.
2
.
4
1
6
Decimal Value
0.006
Six thousandths
Fraction Value
6
1000
0.006 = 6/1000
Example: Find the Value of 6 in 2.416
- The 4 is in the tenths place.
- The 1 is in the hundredths place.
- The 6 is in the thousandths place.
- Its value is 0.006, or 6/1000.
The digit 6 is worth six thousandths
Three Decimal Places Mean Thousandths
Count every position after the decimal point, including any zeros.
How to Find the Value of Any Digit
Whenever you are asked for the value of a digit, use the same four-step process.
1
Locate the Decimal Point
Find the decimal point so you know where the whole number ends and the decimal places begin.
2
Count the Position
Count how many places the digit is to the right of the decimal point.
3
Name the Place
Decide whether the digit is in the tenths, hundredths, or thousandths place.
4
Write the Value
Express the digit as a decimal or fraction using its place value.
Worked Example
5.408
- Locate the decimal point.
- The digit 8 is the third digit to the right.
- Therefore, it is in the thousandths place.
- Its value is 0.008 or 8/1000.
Decimals and Fractions Represent the Same Values
Every terminating decimal can also be written as a fraction. The denominator depends on the place value of the last decimal digit.
0.6
6 10
0.35
35 100
0.009
9 1000
2.5
2 + 5 10
Simplify When Appropriate
After writing the fraction, reduce it if possible. For example, 8/10 simplifies to 4/5.
Writing a Decimal in Expanded Form
Expanded form shows the value contributed by every nonzero digit in the decimal.
4.372
Another Example
12.405
Skip Zero-Value Terms
If a digit is zero, its value is zero, so it is usually omitted from expanded form.
Leading Zeros and Trailing Zeros
Zeros can change the value of a decimal—or they can simply act as placeholders. Understanding the difference is important.
Leading Zero
0.07
The zero before the 7 shows there are no tenths. It is a placeholder.
Trailing Zero
2.50
The trailing zero does not change the value. 2.50 = 2.5.
Remember
Zeros between nonzero digits do affect place value, but zeros at the end of a terminating decimal do not change the value.
Common Decimal Place Value Mistakes
Mistake 1
Saying the 7 in 4.372 is worth 7
The 7 is worth 0.07.
Mistake 2
Forgetting to count the decimal places
Always count from the decimal point outward.
Mistake 3
Writing 0.7 instead of 0.07
The zero shows there are no tenths.
Decimal Place Value Checklist
Step 1
Find the decimal point.
Step 2
Count the digit's position.
Step 3
Name the place value.
Step 4
Write the digit's decimal value.
Step 5
Write the matching fraction.
Step 6
Write the decimal in expanded form.
Ready to Practice?
Work through guided decimal place value problems, identify highlighted digits, write decimal values, convert to fractions, and build expanded form.
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