Decimal numbers are the part of numbers that have two parts. The decimal numbers are in the standard form representing integer and non-integer numbers. Generally, the decimal points are written in a fraction which consists of 10, 100, 1000 in the denominators. The numbers that are expressed in the decimal form are called decimal numbers. Let us check the complete concept on decimal in the below article.
Also, Read:
- Correct to Two Decimal Places
- Converting Decimals to Fractions
- Conversion of a Decimal Fraction into a Fractional Number
Decimals – Definition
A decimal number is a number that has two parts. One part has a whole number and the other part is a fractional part. Both parts are separated by decimal points. If 2.48 is a decimal number, then 2 is the whole number and 48 is the fractional part. “.” is the decimal point.
- The digits having in the whole number part are called ones, then tens, then hundreds, then thousands, and so on.
- The places after the decimal point begin with tenths, then hundredths, then thousandths, and so on………
Examples:
(i) In the decimal number 47.25, the whole number part is 47 and the decimal part is .25
(ii) In the decimal number 89.063, the whole number part is 89 and the decimal part is .063
(iii) Take the decimal number 11.056 where the whole number part is 11 and the decimal part is .056
Types of Decimal Numbers
Decimal numbers are classifieds into different types. They are given with definitions and examples explained in detail.
Recurring Decimal Numbers – Recurring Decimal Numbers are Repeating or Non-Terminating Decimals.
Examples of Recurring Decimal Numbers are 2.123123 (Finite) and 4.252525252525… (Infinite)
Non-Recurring Decimal Numbers – Non-Recurring Decimal Numbers are Non Repeating or Terminating Decimals.
Examples of Non-Recurring Decimal Numbers are 5.14812 (Finite) and 2.5428454845…. (Infinite)
Decimal Fraction – Decimal Fraction is the fraction that consists of the denominator as powers of ten.
Examples are 72.66 = 7266/100 and 43.536 = 43536/1000.
Converting a Decimal Number into Decimal Fraction
To convert the Decimal Number into Decimal Fraction, place the 1 in the denominator and remove the decimal point from the given number. The 1 is followed by the number of zeros that are equal to the number of digits given after the decimal point.
Examples:
1. 47.59
The given decimal number is 47.59
47.59 = 4759/100
4 represents the power of 101 that is the tenths position.
7 represents the power of 100 that is the unit’s position.
5 represents the power of 10-1 that is the one-tenth position.
9 represents the power of 10-2 that is the one-hundredths position.
So that is how each digit is represented by a particular power of 10 in the decimal number.
2. 61.27
The given decimal number is 61.27
61.27 = 6127/100
6 represents the power of 101 that is the tenths position.
1 represents the power of 100 that is the unit’s position.
2 represents the power of 10-1 that is the one-tenth position.
7 represents the power of 10-2 that is the one-hundredths position.
So that is how each digit is represented by a particular power of 10 in the decimal number.
Place Value in Decimals
Place value of a number in decimals is the position of every digit that helps to find its value. The position of each digit that before and after the decimal point is different. Check out the below examples to know each digit’s place value.
Examples:
Let us take a number 296.
- The position of “2” is in One’s place, which means 2 ones (i.e. 2).
- The position of “9” is in the Ten’s place, which means 9 tens (i.e. ninety).
- The position of “6” is in the Hundred’s place, which means 6 hundred.
- As we go left, each position becomes ten times greater.
- Hence, we read it as “two hundred ninety-six”.
As each digit, we move to the left side the value becomes 10 times greater than the previous value.
- The tens place digit is 10 times bigger than Ones.
- The hundreds place digit is 10 times bigger than Tens.
If we consider a decimal number, the digits after the decimal points will become 10 times smaller than other digits. The digits present on the left side of the decimal are multiplied with the positive powers of ten in increasing order from right to left. The digits present in the right of the decimal point are multiplied with the negative powers of 10 in increasing order from left to right.
Example:
1. 61.28
The decimal expansion of the given number 61.28 is
[(6 * 10) + (1 * 1)] + [(2 * 0.1) + (5 * 0.01)]
Properties of Decimals
We have given the main properties of the decimal numbers below those are under multiplication and division operations. Check out all the properties of decimals given below.
- When two decimal numbers are multiplied with each other, then the result will be a decimal number.
- When a decimal number and a whole number are multiplied with each other, then the result will be a decimal number.
- If any decimal fraction is multiplied by 1, the product remains the same decimal fraction by itself.
- If any decimal fraction is multiplied by 0, then the product becomes 0.
- When a decimal number divided by 1, then the quotient must be a decimal number.
- Also, when a decimal number is divided by the same number, then the quotient becomes 1.
- If in case, 0 divided by any decimal number, the quotient becomes 0.
- The division of a decimal number by 0 is not applicable and possible as the reciprocal of 0 does not exist.
Arithmetic Operations on Decimals
We can perform addition, subtraction, multiplication, and division operations on Decimals easily. Check out the below concepts to understand different Arithmetic Operations on Decimals.
Addition Operation on Decimals
When you add two decimal numbers, line up the decimal points of the given numbers and add them. If you don’t see a decimal point, then that is only a whole number.
Subtraction Operation on Decimals
Subtraction Operation on Decimals is also similar to the Addition Operation on Decimals. You need to line up the decimal point of the given numbers and subtract the values.
Multiplication Operation on Decimals
Multiplication Operation on Decimals is like integers as if the decimal point not present. Firstly, find out the product and count the number after the decimal point in the given numbers. The count will let you know how many numbers present after the decimal point in the result.
Division Operation on Decimals
The Division Operation on Decimals is simply dividing the given two decimal numbers. Move the decimal points to make them whole numbers. Then, perform the division operation like normal integers.
Decimal to Fraction Conversion
We consider the digits after the decimal point as the tenths, hundredths, thousandths, and so on. Write down the decimal numbers in the expanded form and simplify the values.
Example:
Let us consider a decimal number 5.21
Conver it into a fraction number.
The expanded form of 5.21 is 521 x (1/100) = 521/100.
Fraction to Decimal Conversion
To convert the fraction number into a decimal number, divide the numerator by denominator.
Example: 9/7 is a fraction. If it is divided, we get 1.285714
Decimal Problems with Solutions
Example 1:
Convert 6/10 in decimal form?
Solution:
Given fraction number is 6/10.
To convert fraction to decimal, divide 6 by 10, we get the decimal form.
Thus, 6/10 = 0.6
Hence, the decimal form of 6/10 is 0.6.
Example 2:
Express 2.36 in fraction form?
Solution:
The given decimal number is 2.36
The expanded form of 2.36 is
= 236 x (1/100)
= 236 /100
= 118/50
= 59/25
Hence, the equivalent fraction for 2.36 is 59/25.
Frequently Asked Questions on Decimals
1. What is meant by Decimal?
A decimal is a number that mainly has two parts named as a whole number part and a fractional part separated by a decimal point.
2. What are the different types of decimals?
There are two types of decimals considered. They are
- Terminating decimals (or) Non-recurring decimals
- Non-terminating decimals (or) Recurring decimals
3. Write the expanded form of 85.3?
The expanded form of 85.3 is 80 + 5 + (3/10)
4. How to convert fractions to decimals?
Factions to decimals are converted by dividing the numerator by the denominator value.