Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$Convert the following repeating decimal to a fraction in simplest form. . bar(49) Answer:$

Convert the following repeating decimal to a fraction in simplest form. $\newline$ $. \overline{49}$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Roots of integers

Full solution

Q. Convert the following repeating decimal to a fraction in simplest form.

\newline

. \overline{49}

\newline

Answer:

Assign $x$ as decimal: Let $x$ equal the repeating decimal $0.49$ with $49$ repeating, so we have: $\newline$ $x = 0.494949...$
Multiply by $100$ : To convert this repeating decimal to a fraction, we can multiply $x$ by $100$ , since the repeating part is two digits long. This will shift the decimal point two places to the right, giving us: $\newline$ $100x = 49.494949...$
Subtract to eliminate repeat: Now, we subtract the original $x$ from $100x$ to get rid of the repeating part: $\newline$ $100x - x = 49.494949... - 0.494949...$ $\newline$ $99x = 49$
Solve for x: Next, we solve for x by dividing both sides of the equation by $99$ : $x = \frac{49}{99}$
Simplify the fraction: We can simplify the fraction by finding the greatest common divisor (GCD) of $49$ and $99$ . The GCD of $49$ and $99$ is $1$ , so the fraction is already in its simplest form.

More problems from Roots of integers

Question

Find the real-number root.

\newline

\sqrt{16}

\newline

\newline

Write your answer in simplified form.

\newline

\_\_\_\_

Posted 9 months ago

Question

Find the real-number root.

\newline

\sqrt{\frac{9}{16}}

\newline

Simplify your answer and write it as a decimal or as a proper or improper fraction.

\newline

\_\_\_\_\_

Posted 9 months ago

Question

Find the real-number root using a calculator. Round your answer to the nearest thousandth.

\newline

\newline

Posted 9 months ago

Question

Multiply. Write your answer in simplest form.

\newline

\sqrt{273} \times \sqrt{42}

\newline

Posted 7 months ago

Question

\newline

\sqrt{\frac{63}{4}}

\newline

Posted 9 months ago

Question

Simplify. Rationalize the denominator.

\newline

\frac{-4}{9 - \sqrt{2}}

\newline

Posted 9 months ago

Question

z

\newline

16 = \sqrt{z}

\newline

z =

Posted 9 months ago

Question

Simplify the radical expression.

\sqrt{14x^{14}}

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

Posted 9 months ago

Question

Simplify the radical expression.

\newline

\sqrt{12x^{12}}

\newline

Write your answer in the form

A

\sqrt{B}

A\sqrt{B}

A

B

are constants or expressions in

x

. Use at most one radical in your answer, and at most one absolute value symbol in your expression for

A

\newline

\underline{\hspace{3cm}}

Posted 9 months ago

Question

What is the value of

\sin \left(\frac{5 \pi}{6}\right) ?

\newline

1

\newline

-\frac{\sqrt{3}}{2}

\newline

-\frac{\sqrt{2}}{2}

\newline

\frac{1}{2}

\newline

150

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant