Question

What is the fractional equivalent of the repeating decimal n = 0.1515... ?
Answer the questions to find out.

1. How many repeating digits does the number represented by n have? (2 points)
The number represented by n has infinity repeating digits

2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. (2 points)

3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)

4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)

5. Write n as a fraction in simplest form. Show your work. (2 points)

Answer 1

The number represented by n has 2 repeating numbers and n as a fraction in simplest form is 5/33

1. How many repeating digits does the number represented by n have?

The decimal number is given as:

n = 0.1515....

From the above representation, we can see that the digits 1 and 5 are repeated

Hence, the number represented by n has 2 repeating numbers

Decide on the power of 10 to multiply by, and tell how you identified that number.

The decimal number is given as:

n = 0.1515....

The digits are repeated after the second decimal place.

So, we multiply the decimal by 10 to the power of 2

Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power.

We have

n = 0.1515....

Multiply by 10^2

n * 10^2 = 0.1515.... * 10^2

4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations.

We have:

n * 10^2 = 0.1515.... * 10^2

This gives

n * 10^2 = 15

Divide by 100

n = 15/100

Subtract 1 from the denominator

n = 15/99

5. Write n as a fraction in simplest form.

We have

n = 15/99

Divide 15 and 99 by 3

n = 5/33

Hence, n as a fraction in simplest form is 5/33

Read more about repeating decimals at:

https://brainly.com/question/14118459

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