Glossary
Place value
Also written: place values · positional notation · tenths hundredths
Definition
Place value is the idea that a digit's worth depends on where it sits. The 4 in 40 is worth forty; the 4 in 0.4 is worth four tenths.
Position carries the value
The digit means something different in each of these:
| Number | The 4 is worth |
|---|---|
| four hundred | |
| forty | |
| four | |
| four tenths | |
| four hundredths |
The digit never changed. Only its position did, and position is doing all the work — which is why beats despite having fewer digits.
One rule, both directions
Each place is worth ten times the place to its right, in both directions without interruption.
The decimal point is a marker, not a break in the pattern. That single fact explains why:
- carrying works the same across the point as anywhere else
- multiplying by ten moves every digit one place left
- the “-ths” names are just denominators read aloud
There is no oneths place
The first place right of the point is tenths. A “oneths” place would be the ones place, which already exists on the other side.
Why zeros hold places
The zero is not decoration. It occupies the tenths place so the is pushed into hundredths. Remove it and the number becomes ten times bigger.
A zero on the far right holds nothing open, which is why and are the same number. See decimal place value.
Lessons that use this term
- What Are Exponents? Powers and Bases Explained
What an exponent means, why it is repeated multiplication and not repeated addition, how to read powers aloud, and where exponents sit in order of operations.
- Scientific Notation: Writing Very Large and Very Small Numbers
How to write a number in scientific notation, convert back to standard form, decide the sign of the exponent, and multiply or divide numbers written this way.
- Decimal Place Value: Reading and Writing Decimals
What each place after the decimal point is worth, how to read a decimal aloud, and how to write one in expanded form or as a fraction.
- Comparing and Ordering Decimals
How to compare decimals by working left to right one place at a time, why a longer decimal is not automatically bigger, and how to put a list in order.
- Rounding Decimals to Any Place
How to round a decimal to the nearest whole, tenth or hundredth: find the place, look at the digit after it, and decide whether to round up or keep it.