Test: Number Systems - 1 - Class 9 MCQ

Remainder,

[We have taken individual remainder, which means if 73 is divided by 34 individually, it will give remainder 5, 75 divided 34 gives remainder 7 and so on.]

[We have taken here negative as well as positive remainder at the same time. When 30 divided by 34 it will give either positive remainder 30 or negative remainder -4. We can use any one of negative or positive remainder at any time.]

Required remainder = 32.

Octal to Decimal conversion is obtained by multiplying 8 to the power of base index along with the value at that index position.

(532.2)8 = 5 * 8² + 3 * 8¹ + 2 * 8⁰ + 2 * 8^-1 = (346.25)10

Fractorise 
√12 = √ 4 x 3 = √ 2 x 2 x 3 = 2√3
√27 = √ 9 x 3 = √ 3 x 3 x 3 = 3√3

- A rational number is a number that can be expressed as a fraction where both the numerator and denominator are integers.
- √196 is a rational number because it simplifies to 14/1, which is a fraction where both the numerator and denominator are integers.
- Options B and C are irrational numbers because they cannot be expressed as fractions.
- Option A is a repeating decimal, which can be rational if it eventually settles into a repeating pattern, but without further information, it is not clear if this is the case.

Required answer,

Note:
We have taken integral value only, not the fractional.
For example 146/5 = 29.2 but we have taken 29 and so on.

And we know that the value of 11√2 is greater than 15 so it's value will be positive, And also sum or differences of rational and irrational is irrational

Every rational number is a real number. Real Number is a set of numbers formed by both Rational and Irrational numbers are combined.

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly.

Decimals of this type cannot be represented as fractions, and as a result, are irrational numbers.

0 is an integer and all integers are rational numbers.