Decimal Place Values
The place value system does not stop at the ones column. To the right of the decimal point, positions continue with values that are fractions of one. These are the decimal place values: tenths, hundredths, thousandths, and beyond.
The Decimal Point
A decimal point separates the whole number part (to its left) from the fractional part (to its right).
Decimal Place Value Chart
| Place | Position from Point | Value | As a Fraction |
|---|---|---|---|
| Tenths | 1 right | 0.1 | 1/10 |
| Hundredths | 2 right | 0.01 | 1/100 |
| Thousandths | 3 right | 0.001 | 1/1,000 |
| Ten-thousandths | 4 right | 0.0001 | 1/10,000 |
| Millionths | 6 right | 0.000001 | 1/1,000,000 |
Reading a Decimal Number
Read the whole part, say "and" or "point", then read the decimal digits as a group and name the final place.
Expanded Form for Decimals
| Number | Expanded Form |
|---|---|
| 4.7 | 4 + 0.7 |
| 2.53 | 2 + 0.5 + 0.03 |
| 10.406 | 10 + 0.4 + 0.006 |
Linking Decimals and Fractions
| Decimal | Fraction | Percentage |
|---|---|---|
| 0.1 | 1/10 | 10% |
| 0.25 | 1/4 | 25% |
| 0.5 | 1/2 | 50% |
| 0.75 | 3/4 | 75% |
Comparing Decimals – Common Mistake
More decimal digits does not mean a larger number.
- Decimal places extend the place value system to values less than 1.
- The decimal point separates whole from fractional parts.
- Tenths (0.1), hundredths (0.01), thousandths (0.001) …
- Always align decimal points when comparing or adding decimals.
- Adding trailing zeros after the last decimal digit does not change the value.
Quick Practice
- Write the place value of 8 in 3.084.
- Write 0.067 in expanded form.
- Which is greater: 0.6 or 0.599?
- Convert 3/100 to a decimal.
- Write "fourteen thousandths" as a decimal.
Summary
Decimal place values mirror whole-number place values but extend to the right of the decimal point. Each position represents a fraction whose denominator is a power of 10. Mastering decimal place values is essential for working with money, measurements, percentages and scientific data.