Place value
Place value is the system that assigns a value to each digit based on its position within a number. In the number 3,475.62: the 3 is in the thousands place (3,000), 4 in the hundreds (400), 7 in the tens (70), 5 in the ones (5), 6 in the tenths (0.6), and 2 in the hundredths (0.02). Each position is ten times greater than the one to its right. This 7th grade foundational math concept from Saxon Math Course 2 is the basis for all number operations, decimal arithmetic, and scientific notation used throughout middle and high school science.
Key Concepts
Property In our number system, the place a digit occupies has a value called place value. Places to the left of the decimal point increase in value (ones, tens, hundreds), while places to the right decrease in value (tenths, hundredths, thousandths).
Examples In the number $28.156$, the digit $5$ is in the hundredths place, so its value is $\frac{5}{100}$. In the number $40.2$, the $4$ is in the tens place and the $2$ is in the tenths place. In the number $3.14159$, the digit $9$ is in the hundred thousandths place.
Explanation Place value is like a number's home address! To the left of the decimal point live the big whole numbers, getting larger the further they go. To the right live the tiny fractions, getting smaller and smaller. The decimal point is the main street separating the two neighborhoods. Knowing the address tells you a digit's true worth.
Common Questions
What is place value?
Place value is the value given to a digit based on its position in a number. In 3,475: the 3 means 3,000, the 4 means 400, the 7 means 70, and the 5 means 5 — determined by each position.
How does place value work with decimals?
Positions to the right of the decimal point are tenths, hundredths, thousandths, etc. In 0.356: 3 is in the tenths place (0.3), 5 in hundredths (0.05), 6 in thousandths (0.006).
Why is place value important in math?
Every arithmetic operation — addition, subtraction, multiplication, division — relies on place value. Aligning decimal points, carrying, and borrowing all depend on understanding what each digit position means.
What grade covers place value?
Place value is foundational and reviewed throughout middle school. In 7th grade Saxon Math Course 2, it underpins decimal operations, ordering numbers, and reading large or small quantities.
How many times greater is the thousands place than the hundreds place?
Each place is 10 times greater than the place to its right. Thousands is 10 times hundreds. Going the other direction, each place is 1/10 of the place to its left.
How does place value connect to scientific notation?
Scientific notation expresses numbers using powers of 10, which directly reflects place value. A number in scientific notation is essentially a single-digit number times its place value position.