This post contains the funs and facts of Decimal Number System, Base, Exponent, Power, Expanded form of decimal numbers, Integral part and Fractional part of decimal numbers, Scientific Notation, Terminating, Non-Terminating Decimal Numbers, Repeating Non-Terminating and Non-Repeating Non-Terminating Decimal Numbers. Question-Answers for all competitive viewers and New children who try to know the mathematics in easy way.
Number System:
The number system is a mathematical value that helps count or measure object, length, volume etc. It helps to perform various mathematical calculation such as addition, subtraction, multiplication and division. It also helps in database processing in computer with the help of central processing unit (CPU).
A number system is defined as a system of infinite number with the help of specific digits or symbols. It represents uniqueness of each and every number. It helps for arithmetic, algebraic and data processing calculation. In other ways, it helps in engineering like Civil Engineering, Mechanical Engineering etc.
There are following types of number system.
| 1. Decimal Number System (Base-10) |
| 2. Binary Number System (Base-2) |
| 3. Octa Number System (Base-8) |
| 4. Hexadecimal Number System (Base-16) |
We are using Decimal Number System in daily life for calculating the data such Addition, Subtraction, Multiply, Division and Data Processing in computer. We will discuss the Decimal Number System in details here, further, We will discuss all other Number System in details later.
Here we can explain the Base, Exponent and Power
| Base: Let see the example 45 , 106 , 23 …..etc. Here 4, 10 and 2 are the base. |
| Exponent: Let see the example 34.5 x 1016 Here Exponent is 16 of the base 10. Exponent is the number, Base is multiplied exponent numbers times itself. |
| Power: Power is an expression that shows the repeated multiplication of the same number or factor. Same number or factor is the base and Number of times multiplied is the Power. i.e. 3x3x3x3x3x3=3 is raised to the power 6=36. |
Decimal Number System:-
It contains only 10 digits to form an Infinite Numbers in series. In Decimal Number System, only ten digits i.e. 0,1,2,3,4,5,6,7,8,9,0. A digit’s value in a Decimal Number System depends on its position. Each digits moves from right to left and it is 10 times greater than its previous digit in a Decimal Number System.
Let see the example of the following numbers. i.e. 96758
| #8 is at ones place. It means 1 one. Ones place number is multiplied by 1. i.e. 1×8=8 |
| #5 is at tens place. It means 1 ten. Tens place number is multiplied by 10. i.e. 10×5=50 |
| #7 is at hundreds place. It means 1 hundred. Hundreds place number is multiplied by 100. i.e. 100×7=700 |
| #6 is at thousands place. It means 1 thousand. Thousands place number is multiplied by 1000. i.e. 1000×6=6000 |
| #9 is at ten thousands place. It means 10 thousand. Ten thousands place number is multiplied by 10000. i.e. 10000×9=90000 |
The number 96758 is written in the expanded form:
| ∴ (9×104)+(6×103)+(7×102)+(5×101)+(8×100) |
| =90000+6000+700+50+8 |
| =96758 |
It is used extensively in everyday life to carry out routine to take such as buying Groceries, Trading, Mathematics, Computer Science, Physics……etc. The decimal system is also referred as Hindu-Arabic System. It is also used for Addition, Subtraction, Multiplication, Division……
The Decimal Number System includes two parts. It consists a decimal point between whole integers and fractional part.
| Integral Part |
| Fractional part |
Let an example of Decimal Number System. Which consist decimal point between integer and fraction part. i.e. 3.5
Integer part: Number System with Funs and Facts
Here integer part is 3 before the decimal point. Its value depends on the position in decimal number before the decimal point.
Let some more examples:
| 345.45 Here whole integer part is 345. It moves right to left ten times to the previous digits. It means 3 at hundreds place, 4 at tens place and 5 at ones place. Hence it is equal to Three hundreds Forty five (345). |
Fraction part: Number System with Funs and Facts
Here fraction part is 68 after the decimal point. Its value also depends on the position in decimal number after the decimal point. It means 0.68, it is always smaller than 1. Hence, 0.68=(6/10)+(8/100)
Let an example of Decimal Number System. Which consist decimal point between integer part and fraction part. i.e. 45.68
| Let some more examples: 345.45 Here fractional part is 0.45. each digit moves from left to right is 1/10 times to the previous digits. It means 4 at tenth place, 5 at hundredth place. Hence it is equal to 0.45. Hence, 0.45=(4/10)+(5/100). |
Fractional part is also written in this form also: 0.5=1/2; 0.75=3/4
Scientific Notation of Decimal Number System
Scientific Notation is a short form of either a very large number or a very small number in the multiplication form. It is easy to write in this form and save the time and a piece of paper. It is very difficult to represent the actual form of a large decimal number. Hence we use scientific notation. The general representation of scientific notation is: y x 10z ; where 1≤y≤10
Let some examples to elaborate the decimal number into scientific notation:
| 345000000000.0=3.45×1011 Here, decimal point shift from right to left is equal to the exponent of 10. i.e. 11 Hence, exponent is positive. |
| 0.000000325=3.25 x 10-7 Here decimal point shift from left to right is equal to the exponent of ten. i.e. 7 Hence, exponent is negative. |
Types of Decimal Number System
| Terminating Decimal Number: Terminating decimal number has an end digit or finite number of digit after the decimal point in decimal number. i.e. 4/5=0.8; 3/4=0.75; 1/2 =0.5…….etc |
| Non-Terminating Decimal Number: Non-Terminating Decimal Number has not end digit or infinite number of digit after the decimal point in decimal number. i.e. 1/3=0.3333……; 1/9=0.11111…..etc |
Non-Terminating Decimal Number: There are two types of Non-Terminating Decimal Number
| Non-Terminating and Repeating Decimal Number: It is also known as Rational Number. It can be represented in the form of p/q, Where p and q are the Real Number and q≠0. i.e. 22/7 is a rational number But, π is a irrational number. Recurring Number: It is also denoted as a bar on the top of repeating part. i.e. 1/3=0.3333……=0.3¯ |
| Non-Terminating and Non-Repeating Decimal Number: It is also known as Irrational Number. i.e. √2=1.41421….. |
Number System with Funs and Facts
Q: Find out the whole integer part from the following decimal number?
| 1. 34.45 2. 45.67 3. 86.34 4. 98.56 5. 78.34 |
Q: Find out the fractional part from the following decimal number?
| 1. 34.45 2. 45.67 3. 86.34 4. 98.56 5. 78.34 |
Q: Write the following decimal number in the decimal form?
| 1. 3/100 2. 4/25 3. 1/2 4. 3/4 5. 4/5 |
Q: Write the following decimal number in fraction form?
| 1. 0.75 2. 0.5 3. 0.16 4. 0.8 5. 0.25 |
Q: Write the following number in expanded form?
| 1. 345 2. 6768 3. 54566 4. 785985 5. 9670897 |
Q: Prove that 0.999…..= 1
| Let x = 0.999…..(i) |
| Equation (i) is multiplied by 10 |
| 10x = 9.999…….(ii) |
| Equation (ii) – Equation (i) |
| (10x-x) = (9.999….- 0.999….) = 9 |
| 9x = 9 |
| x = 1 |
Q: Write the following decimal number in the scientific notation form?
| 1. 0.000000345 2. 680000000 3. 0.000000405 4. 34500000 5. 786000000000 |
For General Knowledge || funs and facts of Prime, Composite, Co-prime Numbers ||