Question

.16666… as a fraction

Answer 1

Therefore, Therefore, the recurring decimal 0.16666... is equivalent to the fraction 1/6.

Explanation:

To express the recurring decimal 0.16666... as a fraction, we can use the concept of infinite geometric series. Let's denote the repeating decimal as x:

x = 0.16666...

Multiplying both sides of the equation by 10, we get:

10x = 1.66666...

Now, let's subtract the original equation from this new equation:

10x - x = 1.66666... - 0.16666...

This simplifies to:

9x = 1.5

Dividing both sides of the equation by 9, we find:

x = 1.5/9

Simplifying the fraction, we have:

x = 1/6

Answer 2

The decimal number 0.16666... can be expressed as a fraction. To convert this decimal to a fraction, we can use the method of infinite geometric series.

Let's call the repeating decimal 0.16666... as x.

Multiply both sides of this equation by 10 to get rid of the decimal point:

10x = 1.66666...

Next, subtract the original equation from the one we just obtained to eliminate the repeating part:

10x - x = 1.66666... - 0.16666...

Simplifying this equation gives:

9x = 1.5

Now, divide both sides of the equation by 9 to solve for x:

x = 1.5/9

Simplifying further, we get:

x = 1/6

Therefore, the fraction equivalent of the decimal 0.16666... is 1/6.

Explanation:

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