Understand Rational Numbers: Concept & Examples
Understand Rational Numbers
What is a Rational Number?
A rational number is a number that is of the form, where p and q are integers and q ≠ 0. Rational numbers are denoted by Q.
How to identify rational numbers?
To identify if a number is rational or not, check the below conditions.
- It is represented in the form of p/q, where q≠0.
- The ratio p/q can be further simplified and represented in decimal form.
- All whole numbers are rational numbers.
Decimal Representation of Rational Numbers:
Rational numbers can be expressed in the form of decimal fractions.
A rational number can have two types of decimal representations:
- Terminating
- Non-terminating
Terminating Decimals:
Terminating decimals are those numbers that come to an end after a few repetitions after the decimal point.
Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals.
Non-terminating Decimals (repeating):
Non-terminating decimals are those that keep on continuing after the decimal point. They do not come to an end or if they do it is after a long interval.
Example: 1/7= 0.1428571…. which is a non-terminating repeating decimal.
Example 1:
Convert the fraction, 5/8 to a decimal.
So,5/8 = 0.625. This is a terminating decimal.
Example 2:
Convert the fraction 7/12 to a decimal.
7/12= 0.583. This is a repeating decimal.
The bar over the number, in this case, 3, indicates the number or block of numbers that repeat unendingly.
Example 3:
The length and breadth of a rectangle are 7.1 inches and 2.5 inches respectively. Determine whether the area of the rectangle is a terminating decimal or not.
Solution: Given, that the length of the rectangle is 7.1 inches and the breadth of the rectangle = is 2.5 inches.
Area of Rectangle = Length × Breadth = 7.1 inches × 2.5 inches =17.75 inches.
As the number of digits is finite after the decimal point, the area of a rectangle is a terminating decimal expansion.
Example 4:
Write 5/3 in decimal form.
Using the long division method, we will observe the steps in calculating 5/3
.
Therefore, 1.666… is a non-terminating repeating decimal and can be expressed as 1.6.
Exercise:
Classify the following decimal fractions as terminating and non-terminating recurring decimals.
- 0.777…
- 0.777
- 4.7182
- 4.7182
- 9.1651651…….
- 9.165
- 0.52888…….
- 0.528
- 72.13
- 10.605
Concept Map
Related topics
Square 1 to 20 : Chart, Table, Perfect Squares and Examples
Square 1 to 20 When you multiply a number by itself, the result is called a square. And when you’re preparing for exams, you need to have a foundation for algebra and quick mental math because you get a really short time to do your exam. Therefore, learning the squares from one to twenty is […]
Square 1 to 40 : Table, Perfect Squares, Chart and Examples
Square 1 to 40 When you multiply a number by itself, the resulting number is a square, and if you are someone who is either appearing in a competitive exam or just wants to do well in math in school, knowing square 1 to 40 is a really important skill. But manually multiplying every time, […]
Square Root : Definition, Formula, Methods and Types Explained
Square Root Square roots are one of those seemingly daunting maths topics that appear in many different situations, from algebra to geometry. Yet the concepts behind them aren’t as hard to grasp. It makes handling numbers far easier if you know the concept well. Let us understand how to find the square roots of a number […]
Cubes 1 to 20 : Chart, Table, Memory Tricks and Examples
Most students don’t struggle much with smaller cubes like 2³ or 3³. Those usually come quickly. The hesitation starts with numbers like 11³ or 17³. Or when someone suddenly asks, what is 20 cubed? That pause is not a memory problem. It’s about the lack of proper understanding and hence confidence. Naturally, learning cubes 1 […]
Other topics
Comments: