The document Short Answers - Number System Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.

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**Ques 1. Find a rational number between 1 and 2.****Solution**: Let x = 1 and y = 2, then

Thus, 3/2 is a rational number between 1 and 2.**Ques 2. Write a rational number equivalent to 5/9 such that its numerator is 25.****Solution:** ∵

Thus, 25/45 is the required rational number whose numerator is 25.**Ques 3. Find two rational numbers between 0.1 and 0.3.****Solution: **Let x = 0.1, y = 0.3 and n = 2

∴ Two rational numbers between 0.1 and 0.3 are: x + d and x + 2d

⇒

⇒

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⇒ **Ques 4. Express **** in the form of decimal.**

**Solution:** We have

Now, dividing 25 by 8, we have:

Since, the remainder is 0.

∴ The process of division terminates.

**Ques 5. Express as a rational number. Solution:** Let x = = 0.3333 ... ...(1)

Multiplying by 100, we have 100x = 100 x 0.3333…

⇒ 100x = 33.3333 … ...(2)

Subtracting (2) from (1), we have

100x – x = 33.3333… – 0.3333…

⇒ 99x = 33**Ques 6. Simplify: (4+ **√3**) (4 −**√3**)****Solution: **(4 +√3) (4 −√3) = (4)^{2} – ( √3)^{2} [∵ (a + b)(a – b) = a^{2} – b^{2}]

= 16 – 3 = 13

Thus, (4 +√3) (4 −√3) = 13**Ques 7. Simplify: (**√3** +**√2)^{2}**Solution:** (√3 +)^{2} = (√3)^{2} + √2 ( √3 ×2) + (√2)^{2 } [∵ (a + b)^{2} = a^{2 }+ 2ab + b^{2}]

= 3 + 2 √6 + 2 = 5 + 2 √6

Thus, (√3 +**(**√2)^{2} = 5 + 2√6**Ques 8. Rationalise the denominator of ****Solution:** Since RF of

Thus, **Ques 9. Find ****Solution:** Since 64 = 4 x 4 x 4 = 4^{3}

**Ques 10. Define a non-terminating decimal and repeating decimals ?****Solution:** The decimal expansion of some rational numbers do not have finite number of decimal places in their decimal parts, rather they have a repeating block of digits in decimal parts. Such decimal expansion is called non-terminating and repeating decimal.

**Example: ****Ques 11. What is the difference between "pure recurring decimals" and "mixed-recurring decimals."?****Solution: **A decimal in which all the digits after the decimal point are repeated, is called a pure recurring decimal. A decimal in which at least one of the digits after the decimal point is not repeated and then some digit(s) repeated is called a mixed recurring decimal.**Example:** are pure recurring decimals.

are mixed recurring decimals.**Ques 12. What type of decimal expansion does an irrational number have?Solution**: The decimal expansion of an irrational number is "non-terminating non-recurring."

Obviously x < y

A rational number lying between x and y

Hence, 7/20 is a rational number lying between

∴

∴

∴ Three required numbers between 0 and 0.1 are: (x + d), (x + 2d) and (x + 3d)

Now

Thus, three rational numbers between 0 and 0.1 are: 0.025, 0.050 and 0.075.**Ques 14. Express **** as a fraction in the simplest form.****Solution:** Let x = = 0.24545 ... ...(1)

Then, multiplying (1) by 10,

we have 10x = 10 x 0.24545...

⇒ 10x = 2.4545 ... ...(2)

Again multiplying (1) by 1000,

we get 1000 x x = 0.24545... x 1000

⇒ 1000x = 245.4545 ... ...(3)

Subtracting (2) from (3),

we have 1000x – 10x = 245.4545... – 2.4545...

⇒ 990x = 243

⇒

Thus **Ques 15. If x = (2 +**√5**) , find the value of** **Solution: **We have x = 2 + √5

∴

∴

Now

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