Place Value and Face Value The Key to Understanding Number Systems
Table of Contents
What is Place Value?
The foundation of our entire number system is place value. The place value of each digit in a number is unique and a digit’s value in a number depends on where it appears in the number.
Let’s say the value of 1 in 710 is 10 here, in the same way, the value of 1 in 1987 is 1,000, that is a thousand here. We can see that although the digits in both numbers are the same, their place value changes as a result of their position.
Understanding the Concept of Ones, Tens, Hundreds
Each place represents 10 times the value of the place to its right in the standard system, also known as the base ten number system (or decimal system).
The following larger unit is the ten, which is composed of 10 ones. One of the subsequent larger units, hundreds, is composed of ten of those units. This pattern is true for decimal quantities of higher (ten hundreds = one thousand).
Place Value Chart
A place value chart can be used to verify that the numbers are placed correctly. For operations to be learned, one must have a solid concept of place value. We can compare numbers, arrange them vertically, and comprehend addition, subtraction, multiplication, and division with larger numbers thanks to it. It also acts as the foundation for regrouping (“borrowing” and “carrying”).
The most widely used place value charts fall into two categories:
- Indian place value chart
- International place value chart
Indian Place Value Chart [Infographic]
The Indian system place value chart is a table that is used in conjunction with the Indian numeral system to establish the relative worth of each digit in a number. This place value chart breaks down a 10-digit number into phases of ones, thousands, lakhs, crores, and so forth. These numbers are separated with commas according to the 2:2:3 rule. This implies that, starting on the right, the first comma should be placed after three digits, followed by commas after two digits.
For example: 97,22,42,643
International Place Value Chart [Infographic]
The International Numerical System is used globally by humans to count in quantities of one, ten, hundreds, thousands, ten thousand, hundred thousands, million, and so forth. This place value diagram divides the numbers into phases of ones, thousands, millions, and so on. Each group of three numerals is separated by a comma, beginning on the right.
Look at the commas in the following number.
For instance: 995,963,762.
Difference Between Place Value and Face Value
The placement of a digit in a given number is indicated by its place value. Contrarily, the number’s face value represents its true worth.
Let’s understand this with the help of an example, 8542.
Decimal Place Value Chart
The decimal place value chart shows the place values of the digits in a decimal number. In a decimal number system, a decimal point is used to denote both whole numbers and fractions. Between the fractional and whole number parts, this decimal point is located. The numbers immediately to the right of the decimal point have a slightly different place value than the rest of the number, which is written using the usual system of ones, tens, hundreds, and so on. Starting at tenths, the place values increase to hundredths, thousandths, and so on as we go farther from the decimal point moving to the right.
Example of Place Value and Face Value
- If 9 is the given number, the face value of 9 is 9, and the place value of 9 is also 9 (9 ones = 9 × 1 = 9).
- For a given number 56, the face value of 5 is 5 and its place value is 50 (5 tens = 5 × 10 = 50).
- For 52169, the face value of 1 is 1 while its place value is 100 (1 hundred = 10 tens × 10 = 100).
Write the Place Value of the Underlined Digit