Solved on Aug 31, 2023

Find the decimal equivalent of the repeating decimal $3.0\overline{1}$ .

STEP 1

Assumptions1. The given number is a repeating decimal, $3.0\overline{1}$ , which means that the digit1 repeats indefinitely after the decimal point.

STEP 2

Let's represent the repeating decimal as a variable, $x$ .
$x =.0\overline{1}$

STEP 3

To eliminate the repeating part, we multiply both sides of the equation by a power of10 that shifts the decimal point to the right of the repeating part. In this case, we multiply by10.
$10x =31.\overline{1}$

STEP 4

Now, we subtract the original equation from the new one to eliminate the repeating decimal.
$10x - x =31.\overline{1} -3.0\overline{1}$

STEP 5

implify the left side of the equation.
$9x =31.\overline{1} -3.0\overline{1}$

STEP 6

implify the right side of the equation. The repeating decimals cancel out.
$9x =28$

STEP 7

Finally, solve for $x$ by dividing both sides of the equation by9.
$x = \frac{28}{9}$ So, $3.0\overline{1} = \frac{28}{9}$ .

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Find the decimal equivalent of the repeating decimal $3.0\overline{1}$ .

STEP 1

Assumptions1. The given number is a repeating decimal, $3.0\overline{1}$ , which means that the digit1 repeats indefinitely after the decimal point.

STEP 2

Let's represent the repeating decimal as a variable, $x$ .
$x =.0\overline{1}$

STEP 3

To eliminate the repeating part, we multiply both sides of the equation by a power of10 that shifts the decimal point to the right of the repeating part. In this case, we multiply by10.
$10x =31.\overline{1}$

STEP 4

Now, we subtract the original equation from the new one to eliminate the repeating decimal.
$10x - x =31.\overline{1} -3.0\overline{1}$

STEP 5

implify the left side of the equation.
$9x =31.\overline{1} -3.0\overline{1}$

STEP 6

implify the right side of the equation. The repeating decimals cancel out.
$9x =28$

STEP 7

Finally, solve for $x$ by dividing both sides of the equation by9.
$x = \frac{28}{9}$ So, $3.0\overline{1} = \frac{28}{9}$ .

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Find the decimal equivalent of the repeating decimal 3.01‾3.0\overline{1}3.01.

STEP 1

Assumptions1. The given number is a repeating decimal, 3.01‾3.0\overline{1}3.01, which means that the digit1 repeats indefinitely after the decimal point.

STEP 2

Let's represent the repeating decimal as a variable, xxx.x=.01‾x =.0\overline{1}x=.01

STEP 3

To eliminate the repeating part, we multiply both sides of the equation by a power of10 that shifts the decimal point to the right of the repeating part. In this case, we multiply by10.10x=31.1‾10x =31.\overline{1}10x=31.1

STEP 4

Now, we subtract the original equation from the new one to eliminate the repeating decimal.10x−x=31.1‾−3.01‾10x - x =31.\overline{1} -3.0\overline{1}10x−x=31.1−3.01

STEP 5

implify the left side of the equation.9x=31.1‾−3.01‾9x =31.\overline{1} -3.0\overline{1}9x=31.1−3.01

STEP 6

implify the right side of the equation. The repeating decimals cancel out.9x=289x =289x=28

STEP 7

Finally, solve for xxx by dividing both sides of the equation by9.x=289x = \frac{28}{9}x=928​So, 3.01‾=2893.0\overline{1} = \frac{28}{9}3.01=928​.

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Find the decimal equivalent of the repeating decimal $3.0\overline{1}$ .

Assumptions1. The given number is a repeating decimal, $3.0\overline{1}$ , which means that the digit1 repeats indefinitely after the decimal point.

Let's represent the repeating decimal as a variable, $x$ .
$x =.0\overline{1}$

To eliminate the repeating part, we multiply both sides of the equation by a power of10 that shifts the decimal point to the right of the repeating part. In this case, we multiply by10.
$10x =31.\overline{1}$

Now, we subtract the original equation from the new one to eliminate the repeating decimal.
$10x - x =31.\overline{1} -3.0\overline{1}$

implify the left side of the equation.
$9x =31.\overline{1} -3.0\overline{1}$

implify the right side of the equation. The repeating decimals cancel out.
$9x =28$

Finally, solve for $x$ by dividing both sides of the equation by9.
$x = \frac{28}{9}$ So, $3.0\overline{1} = \frac{28}{9}$ .