Irrational Numbers

Q. Convert into vulgar fraction:
$2.\overline{23}$

Q. $\frac{3}{0}\text{is a rational number.}$

1. True
2. False

Q. How do you find the derivative of $y=\sqrt{x}$?

Q. Peter and Billy are solving a maths problem and they need to use $\pi$ in their calculation. They started discussing that pie is either rational or irrational number. Peter said that it is rational because we can write it in fraction as $\pi =\frac{22}{7}$ and Billy said that it is irrational because $\frac{22}{7}$ is its approximate value whereas the original value is 3.14159..... Who is correct ?

1. Peter
2. Billy

Q. -1.4 is the same as

1. $-1\frac{2}{5}$
2. $-2\frac{1}{5}$
3. $-1\frac{4}{5}$
4. $-5\frac{1}{4}$

Q.

Write the following numbers in the form $\frac{\mathrm{p}}{\mathrm{q}}$ where $\mathrm{q}$ is a positive integer.

$-3\frac{5}{6}$

Q.

Divide

$2.05by5000$

Q.

Divide

$946.1by1000$

Q. Q.(a) Without actual division, determine if $\frac{-28}{250}$ is terminating or non terminating decimal number.

Q.

State whether the following statement is true or false:

$3\mathrm{kg}200\mathrm{g}=3.2\mathrm{kg}\boxed{}$

1. True
2. False

Q. Ben says $\pi$ is a rational number as it equals the fraction $\frac{22}{7}.$ Max says that $\pi$ is irrational as its value is 3.14159... and that $\frac{22}{7}$ is only an approximation.

Choose the correct option.

Q. Help Sana identify the smallest natural number that can be multiplied with the fraction $8\frac{1}{15}$ such that the decimal expansion of the resulting fraction is terminating.

Q. All rational numbers are integers.

1. True
2. False

Q. Which of the following iS $INCORRECT$?

1. If $x$is a rational number, such that the prime factorisation of denominator is not in the form $2^n{5}^m$, (where $m$ and $n$ are non-negative integers), then it has a decimal expansion which is non-terminating and repeating.
2. $5+\sqrt{2}$ is an irrational number.
3. Every composite number can be expressed as a product of primes.
4. None of these

Q. Why it is called that a pi is irritating number
It doesnt repeat but the fig shows something else

Q. Who used to represent fractions through the given symbol?

1. Arabs
2. Babylonians
3. Egyptians
4. Indians

Q. The fundamental arithmetical operation on 2 recurring decimals can be performed directly without converting them to vulgar fraction

1. Only in addition and subtraction
2. Only in addition and multiplication
3. Only in addition, subtraction and multiplication
4. In all the four arithmetical operations.

Q. State True or False:

1. True
2. False

Q. Which option is representing an irrational number?

1. $3\cdot 14159265\dots$ and $\frac{1}{2}$
2. 1⋅414213… and 3⋅14159265…
3. 2.4444 and $\frac{2}{3}$
4. 0 and 1⋅414213…

Q. Find the number of digits in the square root of 2043.04

1. 2
2. 5
3. 3
4. 4