What is digit?
There are 10 symbols in the number system which are used to write any number in mathematics. These ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 when are used to represent any numbers, these ten symbols are called Digits or Figures.
What is face value in maths?
The Face Value of a digit in a number is equal to the same digit itself. It is also known as true value. The face value of a digit is always equal to the digit itself.
What is face value of each digit in the number 34872?
Face value of 3 in number 34872 is 3.
Face value of 4 in number 34872 is 4.
Face value of 8 in number 34872 is 8.
Face value of 7 in number 34872 is 7.
Face value of 2 in number 34872 is 2.
“Value of place” of a digit in number
To find the value of place 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. As we move from right to left in a number, we keep on increasing the number of zeros by one behind the digits. These 1, 10, 100, 1000 and so on are called value of place in the number.
What is the value of place of 3 and 8 in 543180?
8 is at 2nd position from left, therefore the value of position of 8 = 10
3 is at 4th position from left, therefore the value of position of 3 = 1000
“Place value” of a digit in number
Place Value is a value of digit in the number and it is also known as local value.
How to calculate the place value of a digit?
To find the place value of the digit at a position multiply the face value by the value of place.
Place value = Face value X Value of place
What is the place value of each digit 6, 9 and 4 in the number 26749?
Start moving from left to right in number 26749.
Position of the digits 6, 9 and 4 in 26749 are 1000s, 1s and 10s
6 is at 1000s place, so 6 × 1000 = 6000
9 is at 1s place, so 9 × 1 = 9
4 is at 10s place, so 4 × 10 = 40
So, the place values are:
Place value of 6 is 6000
Place value of 9 is 9
Place value of 4 is 40
What is the face value, value of place and place value of digit 4 in number 15234288?
Face Value of 4 in number 15234288 is 4:
Value of place of 4 in number 15234288 is 1000
We know Place value = Face value X Value of place
∴ Place value of 4 × 1000 = 4000
Place value of repeating digits
If a digit appears more than one time in a number, the place value of that digit will be different for its different positions in the number. Let’s understand it with an example.
What is the place value of repeating digit 6 in 20166498?
6 repeats two times at 4th and 5th positions
Value of place of 6 at 4th and 5th positions are 1000 and 10000 respectively.
Place value of 6 at 1000s place = 6 × 1000 = 6000
Place value of 6 at 10000s place = 6 × 10000 = 60000.
Therefore, the repeating digit 6 has two different place values 6000 and 60000 in the same number
20166498.
Comparison of two numbers with place values
In the chapter,
Unit, Number, Numeral and Number System,
we learnt how to write counts of a thing using numbers along with their units.
So how to compare numbers if one is bigger than the other?
The place value helps in comparing two or more numbers to check which is the greatest number or which is
the smallest number.
1. Numbers with unequal number of digits
The number which has more digits than the other number, will also be greater than the other number. This is a good thumb rule to compare two numbers which have different number of digits.
Which is costlier, a watch with price tag of $20 or $200?
Two watches with a price tag of $20 or $200 have different numbers of digits.
20 has two digits which are 2 and 0. 200 has three digits which are 2, 0 and 0.
So, 200 is greater than 20 because 200 has more digits than 20.
That means a $200 watch is costlier than a $20 watch.
2. Numbers with equal number of digits
When two numbers have equal number of digits then they are compared using the place value of the leftmost digit. If the leftmost digit’s place value of first number is greater than the place value of the leftmost digit of second number then the first number is greater than the second number.
Which number is greater 246 or 514?
246 and 514 have equal numbers of digits i.e. 3
Step 1: Take the leftmost digit of 246 which is 2.
Step 2: Find the place value of 2, which is 2 × 100s = 200
Step 3: Take the leftmost digit of 514 which is 5.
Step 4: Find the place value of 5, which is 5 × 100s = 500
Step 5: Compare 200 and 500, which is greater? It is 500.
That means 514 is greater than 246.
In the above example of two numbers 246 and 514, the leftmost digits are different i.e. 2 and 5. There can be a case when the first digits of both numbers are the same e.g. 246 and 214. In such numbers where the leftmost digit is the same, move to the next digit to its right and check again which has greater place value using the above method.
Which number is greater 246 or 214?
Both 246 and 214 have equal number of digits i.e. 3 and have the same leftmost digit as 2.
In both numbers place values of the leftmost digit 2 is 2 × 100 = 200.
So move to the next digit at the right of digit 2 in both numbers 246 and 214, which is 4 and 1
respectively.
Both 4 and 1 are in 10th place.
So, the place value of 4 in 246 is 4 × 1 = 40 and place value of 1 in 514 is 1 × 10 = 10.
So, 40 is greater than 10.
That means 246 is greater than 214.
