Question Find the fraction equivalent to the repeating decimal $0.\overline{5}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a repeating decimal $0.\overline{5}$ .
2. We need to find the equivalent fraction from the given options.
3. A repeating decimal can be converted to a fraction using algebraic manipulation.

STEP 2

Let's represent the repeating decimal as $x$ .
$x = 0.\overline{5}$

STEP 3

To eliminate the repeating decimal, we multiply $x$ by 10, since there is only one digit repeating.
$10x = 5.\overline{5}$

STEP 4

Now, subtract the original equation ( $x = 0.\overline{5}$ ) from the new equation ( $10x = 5.\overline{5}$ ) to get rid of the repeating decimal.
$10x - x = 5.\overline{5} - 0.\overline{5}$

STEP 5

Perform the subtraction on the left side of the equation.
$9x = 10x - x$

STEP 6

Perform the subtraction on the right side of the equation.
$9x = 5$

STEP 7

Now, solve for $x$ by dividing both sides of the equation by 9.
$x = \frac{5}{9}$

STEP 8

We have found the equivalent fraction for the repeating decimal $0.\overline{5}$ .
The equivalent fraction is $\frac{5}{9}$ .

Was this helpful?

Question Find the fraction equivalent to the repeating decimal $0.\overline{5}$ .

Studdy Solution

STEP 1

Assumptions
1. We are given a repeating decimal $0.\overline{5}$ .
2. We need to find the equivalent fraction from the given options.
3. A repeating decimal can be converted to a fraction using algebraic manipulation.

STEP 2

Let's represent the repeating decimal as $x$ .
$x = 0.\overline{5}$

STEP 3

To eliminate the repeating decimal, we multiply $x$ by 10, since there is only one digit repeating.
$10x = 5.\overline{5}$

STEP 4

Now, subtract the original equation ( $x = 0.\overline{5}$ ) from the new equation ( $10x = 5.\overline{5}$ ) to get rid of the repeating decimal.
$10x - x = 5.\overline{5} - 0.\overline{5}$

STEP 5

Perform the subtraction on the left side of the equation.
$9x = 10x - x$

STEP 6

Perform the subtraction on the right side of the equation.
$9x = 5$

STEP 7

Now, solve for $x$ by dividing both sides of the equation by 9.
$x = \frac{5}{9}$

STEP 8

We have found the equivalent fraction for the repeating decimal $0.\overline{5}$ .
The equivalent fraction is $\frac{5}{9}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Find the fraction equivalent to the repeating decimal 0.5‾0.\overline{5}0.5.

Studdy Solution

STEP 1

Assumptions1. We are given a repeating decimal 0.5‾0.\overline{5}0.5.2. We need to find the equivalent fraction from the given options.3. A repeating decimal can be converted to a fraction using algebraic manipulation.

STEP 2

Let's represent the repeating decimal as xxx.x=0.5‾x = 0.\overline{5}x=0.5

STEP 3

To eliminate the repeating decimal, we multiply xxx by 10, since there is only one digit repeating.10x=5.5‾10x = 5.\overline{5}10x=5.5

STEP 4

Now, subtract the original equation (x=0.5‾x = 0.\overline{5}x=0.5) from the new equation (10x=5.5‾10x = 5.\overline{5}10x=5.5) to get rid of the repeating decimal.10x−x=5.5‾−0.5‾10x - x = 5.\overline{5} - 0.\overline{5}10x−x=5.5−0.5

STEP 5

Perform the subtraction on the left side of the equation.9x=10x−x9x = 10x - x9x=10x−x

STEP 6

Perform the subtraction on the right side of the equation.9x=59x = 59x=5

STEP 7

Now, solve for xxx by dividing both sides of the equation by 9.x=59x = \frac{5}{9}x=95​

STEP 8

We have found the equivalent fraction for the repeating decimal 0.5‾0.\overline{5}0.5.The equivalent fraction is 59\frac{5}{9}95​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question Find the fraction equivalent to the repeating decimal $0.\overline{5}$ .

Assumptions
1. We are given a repeating decimal $0.\overline{5}$ .
2. We need to find the equivalent fraction from the given options.
3. A repeating decimal can be converted to a fraction using algebraic manipulation.

Let's represent the repeating decimal as $x$ .
$x = 0.\overline{5}$

To eliminate the repeating decimal, we multiply $x$ by 10, since there is only one digit repeating.
$10x = 5.\overline{5}$

Now, subtract the original equation ( $x = 0.\overline{5}$ ) from the new equation ( $10x = 5.\overline{5}$ ) to get rid of the repeating decimal.
$10x - x = 5.\overline{5} - 0.\overline{5}$

Perform the subtraction on the left side of the equation.
$9x = 10x - x$

Perform the subtraction on the right side of the equation.
$9x = 5$

Now, solve for $x$ by dividing both sides of the equation by 9.
$x = \frac{5}{9}$

We have found the equivalent fraction for the repeating decimal $0.\overline{5}$ .
The equivalent fraction is $\frac{5}{9}$ .