Place value chart
A place value chart, also referred to as a place value table, is a way to help illustrate the value of each digit in a numeral. In other words, it shows the value of the digit based on its place in the numeral, hence the name place value.
The most common numeral system used today is the decimal numeral system. A place value chart can be made for any numeral system, but we will focus only on the decimal numeral system. Even within just the decimal numeral system, a place value chart can be constructed in a variety of ways. This is because the chart can have as many or as few places as we want, based on the numeral we are trying to represent.
Examples
Represent the following numerals in a place value chart.
1. 123:
This tells us that 123 has 1 hundred, 2 tens, and 3 ones.
1(100) + 2(10) + 3(1) = 123
2. 87,481.23
This tells us that 87481.23 has 8 ten thousands, 7 thousands, 4 hundreds, 8 tens, 1 one, 2 tenths, and 3 hundredths:
8(10000) + 7(1000) + 4(100) + 8(10) + 1(1) + 2(0.1) + 3(0.01) = 87481.23
As can be seen from the examples above, a place value chart simply labels what place each digit lies in, and can have as many or as few places as necessary. It is helpful for illustrating how the decimal numeral system (as well as other numeral systems) work. The decimal numeral system is a base 10 system, so each place represents a power of 10. Other numeral systems, such as the base 2 system (binary), or the base 16 system (hexadecimal) use different bases.