PPT: Real Numbers

Real Numbers Class 10 PPT

``` Page 4

Check whether 6n can end with the digit 0 for any
natural number n.
If any number to end with zero, it should be divisible by
10 or in other words it should be divisible by 2 and 5 as
10 = 2 × 5
Prime factorization of
It can be observed that in prime factorization of 6 only
contains 2 and 3.
According to uniqueness of Fundamental Theorem of
Arithmetic prime factorization of 6n will not contain 5.
So there is no natural number for which 6n can end with
the digit 0 for any natural number n.
Page 5

Check whether 6n can end with the digit 0 for any
natural number n.
If any number to end with zero, it should be divisible by
10 or in other words it should be divisible by 2 and 5 as
10 = 2 × 5
Prime factorization of
It can be observed that in prime factorization of 6 only
contains 2 and 3.
According to uniqueness of Fundamental Theorem of
Arithmetic prime factorization of 6n will not contain 5.
So there is no natural number for which 6n can end with
the digit 0 for any natural number n.
```

Mathematics (Maths) Class 10

120 videos|463 docs|105 tests

FAQs on Real Numbers Class 10 PPT

 1. What are real numbers?
Ans. Real numbers are the set of all rational and irrational numbers, which includes positive and negative numbers, fractions, decimals, and whole numbers. These numbers can be represented on the number line and are used to measure quantities in the real world.
 2. What is the difference between rational and irrational numbers?
Ans. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, while irrational numbers cannot be expressed as a fraction and have non-repeating, non-terminating decimal representations. Examples of rational numbers include 1/2 and 3/4, while examples of irrational numbers include √2 and π.
 3. How can real numbers be classified?
Ans. Real numbers can be classified into different categories based on their properties. These categories include natural numbers (positive integers), whole numbers (non-negative integers), integers (positive and negative numbers), rational numbers (fractions and terminating/ repeating decimals), and irrational numbers (non-repeating, non-terminating decimals).
 4. Can you give an example of a real number that is not rational?
Ans. Yes, an example of a real number that is not rational is the square root of 2 (√2). It cannot be expressed as a fraction or ratio of two integers and has a decimal representation that goes on infinitely without repeating.
 5. How are real numbers used in real life?
Ans. Real numbers are used in various real-life applications such as measuring distances, time, temperature, money, and quantities. They are also used in scientific calculations, engineering, finance, and many other fields where precise measurements and calculations are required. Real numbers provide a universal language for quantifying and comparing different quantities.

Mathematics (Maths) Class 10

120 videos|463 docs|105 tests

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