Digit, Face Value and Place Value

Introduction

In the chapter, Unit, Number and Numeral, we learnt how to write counts of a thing using units and numerals. Let’s take it to the next step, but how much a thing, in other words, is it more or less in numbers. So how do we compare numbers if one is bigger than the other. Here, comes the concept of Face value and Place value, that helps in understanding the number system in mathematics. Eventually, it clearly helps to know which is cheaper, a watch with a price tag of $20 or $200.

This is not the end, we do numerous mathematical operations on numbers for example addition, subtraction, multiplication and division on numbers. The process involved in handling these arithmetic operations are based on understanding of these basic concepts of place value.

To write any number bigger or shorter we use digits. There are 10 digits in the number system which helps us to write any number in mathematics. When we use ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 to represent any numbers, these ten symbols are called Digits or Figures.

In the above example, which is cheaper, a watch with a price tag of $20 or $200, to compare the two numbers 20 and 200 we should learn before all how the numbers are written using place value and face value. In the next step, let’s learn face value and place value by seeing examples.

What is Face Value?

The Face Value of a digit in a number is equal to the same digit itself and it is also known as true value. The face value of a digit is always equal to the digit itself.

What is Place Value?

Place Value is a value of digit in a number and it is also known as local value. For example, the place value of digit 2 in number 34872 is 2, the place value of 7 is 70 and place value of 8 is 800. You can notice as we move from left to right in 34872 we add that much number of zeros behind the digits.

How?

To find the place value of a digit in a number, we always move from right to left. The first position on the right is called 1s, and read as ones. The second position is 10s and read as tens. The next positions go as 100s and 1000s and so on.
Let’s start moving from left to right in number 34872. As we move, we keep on increasing the number of zeros by one behind the digits.
So, no zero behind 2. One zero behind 7, Two zeros behind 8. Three zeros behind 4. Four zeros behind 3.
Or we can write it as multiply the digits with 1s, 10s, 100s, 1000s and 10000s depending upon their position:

2 is at 1s place, so 2 x 1 = 2
7 is at 10s place, so 7 x 10 = 70
8 is at 100s place, so 8 x 100 = 800
4 is at 1000s place, so 4 x 1000 = 4000
3 is at 10000s place, so 3 x 10000 = 30000

So, we get the place value of each digit in 34872 as 2 of 2 , 70 of 7, 800 of 8, 4000 of 4 and 30000 of 3.
In general we can find the place value of a digit at a position by multiplying the face value by the value of place.

Place value of repeating digits in a number

If a digit appears more than one time in a number, the place value of that number will be different and depends upon its position in the number. Let’s understand it with an example.

How to compare two numbers, which is larger or smaller using place value?

Place value helps us in comparing two or more numbers to check which is the greatest number or which is the smallest number.

Compare two numbers with unequal number of digits

In general, we are aware that the number which has more digits than the other number is greater than the other number. This is a good thumb rule to compare two numbers which have different numbers of digits.

Compare two numbers with equal number of digits

Above we learnt how to compare two numbers with unequal numbers of digits. The same is not the case when the number of digits in two numbers are equal.
We check such numbers using the place value of the left most number. If the leftmost number’s place value is greater than the other then the number is greater also than the other number.

In the above example of two numbers 246 and 514, the leftmost digits are different i.e. 2 and 5. There can be a task to compare two numbers with equal numbers of digits and where the leftmost digits are the same.