Place Value
Place value is the value a digit has because of its position within a number. For example, the digit 5 in the number 350 has a place value of 50 because it sits in the tens place.
Place value is a positional numeration system in which the value of each digit in a number is determined by its position relative to the ones place. Each position represents a power of 10, so moving one place to the left multiplies the value by 10, and moving one place to the right divides it by 10. This system extends in both directions: to the left for whole numbers (ones, tens, hundreds, thousands, ...) and to the right of the decimal point for fractional parts (tenths, hundredths, thousandths, ...).
Key Formula
Where:
- = the position of the digit, where $n = 0$ is the ones place, $n = 1$ is the tens place, $n = 2$ is the hundreds place, and so on
Worked Example
Problem: What is the place value of each digit in the number 4,726?
Step 1: Identify the position of each digit, starting from the right.
Step 2: Multiply each digit by the value of its position.
Step 3: Check by adding all the place values together.
Answer: In 4,726: the 4 has a value of 4,000; the 7 has a value of 700; the 2 has a value of 20; and the 6 has a value of 6.
Visualization
Why It Matters
Place value is the foundation of how our entire number system works. Without it, you couldn't add, subtract, multiply, or divide using standard methods — all of those algorithms rely on lining up digits by their position. It also explains how decimals work: the positions to the right of the decimal point represent tenths, hundredths, and so on, which is essential for dealing with money, measurement, and science.
Common Mistakes
Mistake: Confusing the digit itself with its place value
Correction: The digit 3 in 305 is just the number 3, but its place value is 300. Always multiply the digit by the value of its position.
Mistake: Forgetting that zero holds a place
Correction: In 4,026 the zero in the hundreds place means there are no hundreds, but it keeps the 4 in the thousands place. Removing the zero would change the number entirely.