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Digits in mathematics are the single symbols which are used to signify numbers. It is represented alone or in a combination of digits, also called numbers.
- Numbers are also known as numerals.
- Digits are derived from a Latin word named digiti, which means fingers.
- Numerals such as 0, 1, 2, 3,4, 5,6,7,8,9 are employed to represent a combination of numbers.
- They are considered building blocks of mathematics.
- These digits correspond to the base ten numeral system.
- It performs mathematical operations in our daily lives.
- Money transactions, bank account numbers, and vehicle registrations are all examples of digits.
- For example, the digits 8 and 9 in the number 89 are two separate digits.
Key Terms: Digits, One Digit Number, Two Digit Number, Numbers, Three Digit Number, Four Digit Number, Five Digit Number, Symbols, Number System, Mathematical Operations
What are Digits?
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Digits are individual symbols that join together to form a numeral, which then describes the number. These are building blocks of mathematics that work the same as letters in language.
- Digits tend to exhibit meaning individually as well as in combination with another digit.
- They are divided into face value and place value.
- It is a type of mathematical entity which is equivalent to a numerical value.
- 1 and 9 are the smallest and largest one-digit numbers.
- It is used in calculation and problem-solving techniques.
- Digits are used in mathematics and computer science.
One-digit numbers, two-digit number, numbers, three-digit numbers, four-digit numbers, and five-digit numbers are different types of digits.
Example of What are Digits?Example: Digits can stand alone for singular numerals, such as “7”, which is both a digit and a numeral referring to the number seven.
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Digits
History of Digits
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People used Roman abacus or stone tokens thousands of years ago when the number system was unknown. With the passage of time and breakthroughs in trade between regions and countries, the need for larger denominations became apparent.
- This resulted in the development of number systems as we know them today.
- As nations advanced, so did the need to deal with larger populations.
The distance between the Earth and the Moon, the speed of light, and the size of a microorganism; these enthralling facts instilled in us the desire to expand our number systems.
- As a result, the concept of numbers and digits was developed.
- Counting small numbers is simple process.
Read More:
| Chapter Related Concepts | ||
|---|---|---|
| Cosine Rule | Arithmetic | Definite Integrals |
| Fraction | Degree of polynomial | Number Systems |
Place Value of Digits
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The place value of digits refers to the position or placement of a digit in a number. It starts from unit place and goes on to tens, hundreds, thousands, ten thousand, and so on.
- To identify the correct position of a digit, make use of a place value chart.
- It also specifies how much each digit in the value chart stands for.
Example of Place Value of DigitsExample: Consider the number 4,459. In this number, the digit 5 has a place value of 50 because it’s in the tens place. Similarly, the digit 9 has a place value of 9 because it’s in the unit place. |
Face Value of Digits
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Face Value of digits refers to the actual value of digit that is used in the number. Its value never changes irrespective of its position in the number.
- Face value is used to indicate the inherent worth of a digit.
- It is easier to calculate in the number.
Example of Face Value of DigitsExample: Consider the number 4,459. In this number, the digit 5 has a face value of 5. Similarly, the digit 9 has a face value of 9. |
Read also : Real Numbers: Definition, Properties and Examples
Types of Digits
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There are various types of digits which are as follows:
One Digit Number
One Digit Number as name indicates is used to represent single digit in a number. There are a total 9 single-digit numbers namely 0, 1, 2, 3,4, 5,6,7,8,9. 1 (one) is the smallest one-digit number, and 9 is the biggest one.
Note: When we use a number, all of the digits become numbers.
Example of One Digit NumberExample: 1, 2 3 are all one digit number. |
Two Digit Numbers
Two digit numbers are made of two digits, which are divided into unit place and ten’s place. It starts at 10 and ends at 99. The smallest two-digit number is obtained by adding one unit to the greatest one-digit number.
Example of Two Digit NumbersExample: Addition of two digits 1 and 9 will form a two digit number 10.
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Three Digit Numbers
Numbers are said to form a three digit numbers that consists of three digits. The smallest three-digit number is obtained by adding one unit to the greatest two-digit number.
- 100 is the smallest three-digit number, while 999 is the largest.
Example of Three Digit NumbersExample: Consider a large auditorium with hundreds of people. We can’t possibly count this many people with our fingers alone. We employ numbers up to three digits to deal with such metrics. |
Four Digit Numbers
Numbers are said to form a four digit numbers that consists of four digits. The smallest four-digit number is obtained by adding one unit to the greatest three-digit number.
- 1000 is the smallest four-digit number, whereas 9999 is the largest.
Example of Four Digit NumbersExample: Imagine tens of thousands of people crammed inside a sports pavilion. For example, to deal with such things as the cost of a closet or a bicycle, we use digits up to four digits.
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Five Digit Numbers
Numbers are said to form a five digit numbers that consists of five digits. The smallest five-digit number is obtained by adding one unit to the greatest four-digit number.
- 10000 is the smallest five-digit number, and 99999 is the largest five-digit number.
Example of Five Digit NumbersExample: When dealing with figures as large as a state’s population or the cost of a motorcycle, we need to work with five-digit figures.
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Read More:
| Class 6 Maths Related Concept | ||
|---|---|---|
| Root 2 is an irrational number | Descending Order | Real Numbers Formula |
| Natural numbers | Number Lines | Division of rational expression |
Things to remember
- In mathematics, digits are the single symbols which are used to signify numbers.
- In computer science, the term digits is preferred.
- These digits are known as numerical digits or simply numbers in mathematics.
- One is the smallest one-digit number, while nine is the greatest one-digit number.
- Digits can stand alone for singular numerals.
- To refer to larger values, two or more digits can be combined.
Sample Question
Ques. What is the total number of three-digit numbers that are divisible by six exactly? (3 marks)
Ans. There are 900 three-digit numbers between 100 and 999.
As a result, the smallest three-digit number divisible by six is 6 ×17 = 102, while the largest is 6 × 166 = 996.
As a result, the required number of numbers is 166 - 17 + 1 = 150.
Ques. When the digits of a two-digit number are swapped, the resulting number is 18 higher than the original. The total number of digits is eight. What is the original number's triple value? (3 marks)
Ans. Let's use the letters 'a' and 'b' for the unit and tenth digits, respectively.
As a result, a + b = 8 and a – b = 18 ÷ 9 = 2
So, a = (8 + 2)÷ 2 = 5 and b = 5 – 2= 3
As a result, the needed value is 3 × 35 = 105.
Ques. The sum of a two-digit number is eight times its digits. When 45 is subtracted from the numerals, the digits' positions are reversed. So determine the number ? (3 marks)
Ans. The number is divisible by 8 and the two numbers differ by = 45 ÷ 9 = 5.
Hence, the required number is 72.
Ques. A two-digit number is four times its digits' sum and twice its digits' product. Determine the number? (4 marks)
Ans. Let xy be the two-digit number that is required.
xy = 4(x + y)
10x + y = 4x + 4y
10x - 4x + y - 4y = 0
6x - 3y = 0
2x - y = 0
y = 2x-----------(1)
xy = 2 × x × y
10x + 1y = 2xy -----------(2)
Applying (1) in (2), we get
10x + 1(2x) = 2x(2x)
10x + 2x = 4x2
12x = 4x2
x = 12/4
x = 3
By applying the value of x in (1), we get
y = 2(3)
y = 6
So, 36 is the required two-digit number.
Ques. A two-digit number with a digit product of 21. The digits are reversed when 36 is subtracted from a number. Now, what is the number? (4 marks)
Ans. Assume that xy is the required two-digit number.
The product of the digits of a two-digit number equals 21.
x ? y = 21
y = 21/x ---- (1)
The digits are reversed when 36 is subtracted from a number.
xy - 36 = yx
10x + y - 36 = 10y + x
10x - x + y - 10 y = 36
9x - 9y = 36
Dividing it by 9, we get
x - y = 4 --- (2)
By applying (1) in (2), we get
x - (21/x) = 4
x2 - 21 = 4x
x2 - 4x - 21 = 0
x2 - 7x + 3x - 21 = 0
x(x - 7) + 3(x - 7) = 0
(x - 7) (x + 3) = 0
x - 7 = 0
x = 7
x + 3 = 0
x = -3
By applying the value of x in (1), we get
y = 21/x
y = 21/7
y = 3
Hence, the two digit number is 73 here.
Ques. A two-digit number has a product of digits that equals 12. When the number 36 is added to it, the digits are reversed. Find the figures? (4 marks)
Ans. Let xy represent the required two-digit number.
A two-digit number with the product of its digits equal to 12.
x × y = 12
y = 12/x ---- (1)
The digits are swapped when 36 is added to a number.
xy + 36 = yx
10x + y + 36 = 10y + x
10x - x + y - 10y = -36
9x - 9y = -36
Dividing it by 9, we get
x - y = -4 ---- (2)
By applying (1) in (2)
x - (12/x) = -4
x2 - 12 = -4 x
x2 + 4x - 12 = 0
(x - 2) (x + 6) = 0
| x - 2 = 0 x = 2 | x + 6 = 0 x = -6 |
By applying the value of x in (1), we get
y = 12/x
y = 12/2
y = 6
As a result, the two-digit number required is 26.
Ques. When you add 18 to a two-digit number, you get another two-digit number with reversed digits. How many two-digit numbers are there? (4 marks)
Ans. Let's call the two-digit number 'ab,' and the number formed by adding 18 to it is 'ba.'
So ab + 18 = ba
⇒ (10a + b) + 18 = 10b + a
⇒ 18 = 9b – 9a
⇒ 2 = b – a
We know that ab and ba are both two-digit numbers, hence a, b ≠ 0.
Also when b = 9, a = 7; b = 8, a = 6; b = 7, a = 5; b = 6, a = 4; b = 5, a = 3; b = 4, a = 2; b = 3, a = 1
Hence, Total 7 combinations are possible.
Ques. In the number 4758973, write the digit which is in –
(a) thousands place
(b) hundred places
(c) ten thousand’s place
(d) million’s place? (3 Marks)
Ans. (a) A number in the thousands place is 8
(b) A number in hundred’s place is 9
(c) A number in ten thousand’s place is 5
(d) A number in million’s place is 4
Ques. When the digits of a two-digit number are swapped, the resulting number is 27 higher than the original. The total number of digits is eight. What is the original number's triple value? (3 marks)
Ans. Let's use the letters 'a' and 'b' for the unit and tenth digits, respectively.
As a result, a + b = 8 and a – b = 36 ÷ 9 = 4
So, a = (8 + 4)÷ 2 = 6 and b = 6 – 4= 2
As a result, the needed value is 3 × 26 = 78
Ques. The sum of a two-digit number is eight times its digits. When 54 is subtracted from the numerals, the digits' positions are reversed. So determine the number ? (3 marks)
Ans. The number is divisible by 8 and the two numbers differ by = 54 ÷ 9 = 6.
Hence, the required number is 72.
Ques. What should be the place value and face value of 2 and 8 in 2006987? (3 Marks)
Ans. In the given number, the place value and face value of 2 and 8 are as follows:
Face Value and Place Value of 2
- Face Value: 2
- Place Value: 2000000
Face Value and Place Value of 8
- Face Value: 8
- Place Value: 80
Ques. What is the place value of 8 in 659721? Also, expand the number? (2 Marks)
Ans. The place value of 9 in 458743 is thousands, such that, 9 x 1000 = 9000.
Expanded form of 659743 = 6 x 100000 + 5 x 10000 + 8 x 1000 + 7 x 100 + 2 x 10 + 1.
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