Understanding Decimal Place Values
Learn how each digit in a decimal number has a specific value based on its position.
Definition
- is in the ones place (value: )
- is in the tenths place (value: )
- is in the hundredths place (value: )
- is in the thousandths place (value: )
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Worked Examples
What is the place value of each digit in ?
Identify the ones place
The digit before the decimal point is → is in the ones place (value: )
Identify the tenths place
The first digit after the decimal is → is in the tenths place (value: )
Identify the hundredths place
The second digit after the decimal is → is in the hundredths place (value: )
Identify the thousandths place
The third digit after the decimal is → is in the thousandths place (value: )
Answer:
Common Mistakes
Thinking is greater than because 45 > 5
Why it's wrong: Students compare digits without considering place value. The 5 in is in the tenths place, while 45 represents 4 tenths and 5 hundredths.
Correct: Compare place by place: , so because 5 tenths > 4 tenths.
Reading as 'zero point seven' instead of 'zero point zero seven'
Why it's wrong: The zero in the tenths place is important - it shows there are no tenths.
Correct: Read each digit: 'zero point zero seven' or 'seven hundredths.'
Confusing tenths and tens, hundredths and hundreds
Why it's wrong: The names sound similar but are on opposite sides of the decimal point.
Correct: Tenths () and hundredths () are fractions. Tens () and hundreds () are whole numbers.
Interactive Visual
Place Value Chart
| Thousands 1,000 | Hundreds 100 | Tens 10 | Ones 1 | Tenths 0.1 | Hundredths 0.01 |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
Expanded Form:
1 × 1,000 + 2 × 100 + 3 × 10 + 4 × 1 + 5 × 0.1 + 6 × 0.01
Click on any place value to highlight it and see its value.
Click on numbers to select them. Adjust the range to explore different values.
Interactive Sandbox
Expression Calculator
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History
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Practice Problems
18 problemsIn the number , which digit is in the tenths place?
Why It Matters
- Money: Prices like 4.99 euros use tenths and hundredths (cents)
- Measurements: Your height might be 1.52 meters
- Science: A thermometer may read 36.7 degrees
- Sports: Olympic times are measured to thousandths of a second (9.572 seconds)
Real World Applications
Money and Shopping
Prices use decimal place values to show euros and cents.
Example:
A book costs 12.95 euros. The 9 is in the tenths place (9 ten-cent coins) and the 5 is in the hundredths place (5 cents).
A video game costs 49.99 euros. You pay with a 50 euro note.
How much change do you get?
Step 1: Write the mathematical expression
Calculate:
Athletics and Sports
Race times are measured in seconds with decimal precision.
Example:
A swimmer finishes in 52.48 seconds. The 4 in the tenths place means 4 tenths of a second, and the 8 means 8 hundredths.
Runner A finishes in 10.52 seconds. Runner B finishes in 10.49 seconds.
Who won the race?
Step 1: Write the mathematical expression
Compare: vs
Measurements in Science
Scientists measure very precisely using many decimal places.
Example:
A pencil is 18.5 cm long. A feather weighs 0.003 kg (3 thousandths of a kilogram = 3 grams).
A student measures a leaf at 7.25 cm and a twig at 7.3 cm.
Which is longer?
Step 1: Write the mathematical expression
Compare: vs
Key Takeaways
- 1Decimals use a decimal point to separate whole numbers from parts less than one
- 2Each position after the decimal has a name: tenths (), hundredths (), thousandths ()
- 3The value of a digit depends on its position, not just the digit itself
- 4Moving one place to the right divides the value by 10
- 5Expanded form breaks a decimal into the sum of each place value
Frequently Asked Questions
Glossary
- Decimal
- A number that contains a decimal point, showing values less than one whole
- Decimal point
- The dot (.) that separates the whole number part from the fractional part
- Tenths
- The first place to the right of the decimal point, worth or
- Hundredths
- The second place to the right of the decimal point, worth or
- Thousandths
- The third place to the right of the decimal point, worth or
- Expanded form
- Writing a number as the sum of each digit's place value