Question

convert the following decimals into rational numbers: 1)2.3 if 3 has bar over it

Answer 1

Let x=2.333333.......... . eq. 1
multiplying by 10 on both sides
10x=23.333333....... ...... eq. 2
subtracting equation 1 from equation 2, we get:
9x=21
x=21÷9
x=7/3

Answer 2

The decimal 2.3 with 3 having a bar over it, denoted as $2.\overline 3$ when converted to a rational number becomes 7/3

Step-by-step Explanation

Given a decimal, $2.\overline 3$

To be found: To convert the given decimal into a rational number.

Solution:

A rational number is a number of the form p/q and q is non-zero.

We have the decimal, $2.\overline 3=2.3333...$

Now, take $x=2.3333...$ -----(1)

Next, multiply (1) by 10 on both sides,

$10x=23.3333...$  --------(2)

Next, subtract (1) from (2),

$\implies 10x-x=(23.3333...)-(2.3333...)\\\implies 9x=21\\\implies x=\frac{21}{9}$

Simplifying, we get

$x=\frac{7}{3}$

Therefore, the converted form of the decimal, $2.\overline 3$ into the form of a rational number is $\frac{7}{3}$

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