meet with vaibhav meena
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how to identify decimal number
In Mathematics, the numbers can be classified into different types, namely real numbers, natural numbers, whole numbers, rational numbers, and so on. Decimal numbers are among them. It is the standard form of representing integer and non-integer numbers. In this article, let us discuss in detail about “ Decimals”, its types, properties, and place value representation of decimal numbers with many solved examples.
In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point. The dot present between the whole number and fractions part is called the decimal point. For example, 34.5 is a decimal number.
Here, 34 is a whole number part and 5 is the fractional part.
“.” is the decimal point.
Let us discuss some other examples.
Here is the number “thirty-four and seven-tenths” written as a decimal number:
Types of decimal number
Decimal Numbers may be of different kinds, namely
Recurring Decimal Numbers (Repeating or Non-Terminating Decimals)
Example-
3.125125 (Finite)
3.121212121212….. (Infinite)
Non-Recurring Decimal Numbers (Non Repeating or Terminating Decimals):
Decimal Fraction- It represents the fraction whose denominator in powers of ten.
Example:
81.75 = 8175/100
32.425 = 32425/1000
Converting the Decimal Number into Decimal Fraction:
For the decimal point place “1” in the denominator and remove the decimal point.
“1” is followed by a number of zeros equal to the number of digits following the decimal point.
place value in decimal number
The place value system is used to define the position of a digit in a number which helps to determine its value. When we write specific numbers, the position of each digit is important.
The digits to the left of the decimal point are multiplied with the positive powers of ten in increasing order from right to left.
The digits to the right of the decimal point are multiplied with the negative powers of 10 in increasing order from left to right.
Properties of decimal number
The important properties of decimal numbers under multiplication and division operations are as follows:
If any two decimal numbers are multiplied in any order, the product remains the same.
If a whole number and a decimal number are multiplied in any order, the product remains the same.
If a decimal fraction is multiplied by 1, the product is the decimal fraction itself.
If a decimal fraction is multiplied by 0, the product is zero (0).
If a decimal number is divided by 1, the quotient is the decimal number.
If a decimal number is divided by 1, the quotient is the decimal number.
If a decimal number is divided by the same number, the quotient is 1.
If 0 is divided by any decimal, the quotient is 0.
The division of a decimal number by 0 is not possible, as the reciprocal of 0 does not exist.
aromatic operation on decimal number
Like integers, the arithmetic operations like addition, subtraction, multiplication, and division operation can be performed on decimal numbers. Now, let us discuss important tips while performing arithmetic operations.
addition
While adding decimal numbers, line up the decimal points of the given numbers and add the numbers. If a decimal point is not visible (i.e., whole numbers), the decimal is behind the number.
subtraction
Similar to the addition of decimal numbers, line up the decimal point of the given numbers, and subtract the values. To perform the arithmetic operation, use place holding zeros for our reference.
Multiplication
Multiply the given numbers like integers, as if the decimal point is not present. Find the product and count up how many numbers are present after the decimal point in both the numbers. The count represents how many numbers are required after the decimal point in the product
Division
To simply divide the decimal numbers, move the decimal point in the numbers such that the number becomes the whole numbers. Now, perform the division operation like the integer division.
Decimal to Fraction Conversion
The conversion of decimal to fraction or fraction to decimal values can be performed easily. Now, we will
discuss both the conversion methods below:
Decimal to Fraction Conversion
We know the numbers after the decimal point represents the tenths,
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