2.161616 as fraction and as a mixed number

Mathematics

2 answers:

Svet_ta [12.7K]4 months ago

7 0

Response:

x = $\frac{214}{99}$ , mixed fraction [tex]2\frac{16}{99}[/tex]

Detailed steps:

We are given the value: 2.161616

Objective: express as both a fraction and a mixed number.

Process: Consider x = 2.161616

The digits '16' are repeating in 2.161616

Thus, we denote the repeated section with a bar over 16

By multiplying both sides by 100:

100x = 100 * 2.161616

yielding 100x = 216.1616

Using this, we can express 216.1616 in terms of x

100x = 214 + x

Subtracting x from each side gives

99x = 214

Dividing by 99 leads to

x = $\frac{214}{99}$ .

Mixed fraction form: $2\frac{16}{99}$

Thus, x = $\frac{214}{99}$ , mixed fraction [tex]2\frac{16}{99}[/tex]

babunello [11.8K]4 months ago

3 0

As a fraction, 2.161616 is represented as 2 161616/1000000, and when simplified, it becomes 2 10101/62500.

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