Question

0.42 [bar on 2] when expressed in the form of p/q is

Answer 1

don't multiply eqn1 directly by 100 it will be wrong , hope it helps

Answer 2

Answer:

$x={0.4\bar2}$ is equal to $\frac{19}{45}$

Step-by-step explanation:

Rational number, in arithmetic, a number that can be represented as the quotient $\frac{p}{q}$ of two integers such that $q \neq 0.$ In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.

Conversion of Decimal Number Into Rational Number:
When decimal representation is of non-terminating repeating nature. In a non terminating repeating decimal, there are two types of decimal representations

1. A decimal in which all the digit after the decimal point are repeated. These type of decimals are known as pure recurring decimals.

2. A decimal in which at least one of the digits after the decimal point is not repeated and then some digit or digits are repeated. This type of decimals are known as mixed recurring decimals.

Conversion Of A Pure Recurring Decimal To The Form p/q

Algorithm:

Step-1: Obtain the repeating decimal and pur it equal to x (say)

Step-2: Write the number in decimal form by removing bar from the top of repeating digits and listing repeating digits at least twice. For sample, write $x=\bar{0.8}$ as$x = 0.888$.

Step-3: Determine the number of digits having bar on their heads.

Step-4: If the repeating decimal has 1 place repetition, multiply by 10; a two place repetition, multiply by 100; a three place repetition, multiply by 1000 and so on.

Step-5: Subtract the number in step 2 from the number obtained in step 4

Step-6: Divide both sides of the equation by the coefficient of x.

Step-7: Write the rational number in its simplest form.

Given: Let $x={0.4\bar2}$

$x=0.4222$...........(1)

Multiply equation (1) by 10.

$10x=4.222$....(2)

Multiply equation (2) by 100.

$100x=42.22$....(2)

Subtract equation (2) from equation (1), we get

$100x-10x=42.22-4.22\\90x=38\\x=\frac{38}{90} \\\\x=\frac{19}{45}$

hence, $x={0.4\bar2}$ is equal to $\frac{19}{45}$.

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