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16 days ago

Write 2.3181818... as a mixed number.

Mathematics

2 answers:

Leona [9.2K]16 days ago

4 0

Answer:

x = $\frac{51}{22}$ .

Step-by-step explanation:

Provided: 2.3181818...

Required: to express as a mixed number.

Solution: We are given that

2.3181818...

Let x be equal to 2.3181818...

Notice that the digits 18 are recurring as 18181818......

Thus, the overline is drawn above the two digits 18

$x = 2.318.....$ .

On multiplying each side by 100:

$100x = 100 * 2.318.....$ .

100x equals 231.81818.....

The expression 231.81818..... can be represented in terms of x

Hence, 100x = 229.5 + x

By subtracting x from both sides:

100x - x = 229.5

Thus, 99x = 229.5

When dividing both sides by 99:

x = $\frac{229.5}{99}$ .

x = $\frac{2295}{990}$ .

x = $\frac{459}{198}$ .

x = $\frac{51}{22}$ .

Therefore, x equals $\frac{51}{22}$ .

PIT_PIT [9.1K]16 days ago

3 0

Assuming the sequence persists, let $x=2.3181818\ldots=2.3\overline{18}$ .

Then $10x=23.\overline{18}$ and $1000x=2318.\overline{18}$ , leading us to

$1000x-10x=990x=2295\implies x=\dfrac{2295}{990}=\dfrac{51}{22}$ .

<psince src="https://tex.z-dn.net/?f=51%3D2%5Ccdot22%2B7" id="TexFormula5" title="51=2\cdot22+7" alt="51=2\cdot22+7" align="absmiddle" class="latex-formula">, we can convert $x$ into the mixed number $2+\dfrac7{22}$ . </psince>

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