# Place value

Place value is the value of a digit determined by its position in a number. In the decimal numeration system, the most commonly used numeration system, place value is based on groupings of ten and powers of ten. Each digit ranges from 0-9. Once the value of a digit exceeds 9, 1 is added to the value of the digit to its left. The value of any given digit in a number can be determined by multiplying the digit by the respective power of 10 determined by the position the digit is in.

For example, the number 152 has digits in the ones, tens, and hundreds place (from right to left). We can expand this to see how place values work in a positional numeral system:

152 = 1 × 10^{2} + 5 × 10^{1} + 2 × 10^{0}

Each digit represents a power of 10. The further left, the larger the value. The further right of a decimal point, the smaller the value, also by a power of 10 per digit.

In larger numbers, digits are grouped in threes, where each digit represents one place value. The groups of three digits are referred to as periods, and are typically separated by commas.

Example

Use the following place value chart to determine the value of the digits 7 and 8 in the number 72,486.

The 7 is in the ten thousands place, indicated by the 10^{4}, which equals 10,000. To find the value, multiply 7 and 10,000 to get 70,000.

The 8 is in the tens place. 8 × 10 = 80.

The above figure is an example of a place value chart up to the billions place. It can extend either to the left (larger) or right (smaller). It can be used to quickly determine the place value of any digit in a given number, as we did in the example above.

### Did you know?

Computer scientists use a numeration system in which place value is based on groupings of two and powers of two. The first five numbers in this system, called the base two or binary numeration system, are 0, 1, 10, 11, and 100. Their values in base ten are 0, 1, 2, 3, and 4.

Base two has only two digits: 0 and 1. These digits are used to tell the computer what to do. 0 shows that there is no electrical current and 1 shows tha the current is on. Through the use of many 0s and 1s, computers can perform many complex operations.