Place value
Place value is the value a digit represents based on its position within a number. In the base-10 system, each place is worth ten times the place to its right, so the 5 in 352 represents 50, while the 5 in 3.52 represents 5 tenths.
Place value is the principle that a digit's value depends on where it sits in a number. Our number system is base-10 (decimal), so each position represents a power of ten: moving one place to the left multiplies the value by 10, and moving one place to the right divides it by 10. In the number 4,738, the 4 represents 4,000, the 7 represents 700, the 3 represents 30, and the 8 represents 8.
The same pattern continues past the decimal point. The first place to the right of the decimal is the tenths place, then hundredths, then thousandths. In 6.295, the 2 represents 2 tenths (0.2), the 9 represents 9 hundredths (0.09), and the 5 represents 5 thousandths (0.005). Any number can be expanded as a sum of its place values: 6.295 = 6 + 0.2 + 0.09 + 0.005.
Place value underlies nearly every arithmetic skill. Comparing decimals, rounding to a given place, carrying and borrowing in addition and subtraction, and converting between decimals, fractions, and scientific notation all depend on reading positions correctly. A common error is comparing decimals by digit count — 0.35 is greater than 0.295 even though it has fewer digits, because 3 tenths exceeds 2 tenths.
Place value questions appear on the Praxis Core math test, which covers place value and decimal representation directly, and the concept supports decimal and number-sense questions on the GRE quantitative section and the CLT as well.
Key takeaways
- A digit's value depends on its position: each place is worth ten times the place to its right.
- Places to the right of the decimal point represent tenths, hundredths, and thousandths.
- Any number can be written in expanded form as the sum of its digits' place values.
- Compare decimals place by place from the left — more digits does not mean a larger number.
- Praxis Core tests place value directly, and it underpins decimal questions on the GRE and CLT.