Question

What is 2.7 repeating as a fraction?

Answer 1

²⁵/₉

Further explanation

We will solve the problem of repeating decimals.

Definition:

A decimal number whose decimal part has digits which repeat endlessly is called a repeating decimal.

For example, $\boxed{ \ \frac{4}{33} = 0.121212... \ }$ is a repeating decimal. The three dots mean the digits in the decimal part repeat infinitely.

Notice that when we carry out the division $\boxed{ \ 4 \div 33 \ }$, the quotient never ends (or terminates) because zero never appears as a remainder. The block of two digits, 12, keeps appearing and no other digits appear. Often we use a bar (-) to show the block of digits which repeats in a decimal: $\boxed{ \ \ 0. \overline{12} = 0.121212... \ \ }$

Given:

$\boxed{ \ 2.77777... = 2.\overline{7} \ }$

Question:

Express it as a fractional form.

Problem Solving:

Let $\boxed{ \ x = 2.77777... \ }$

Both sides multiplied by 10.

Then $\boxed{ \ 10x = 27.77777... \ }$

Let us subtract 10x by x. Subtract side by side.

$\boxed{ \ 10x = 27.77777... \ }$

$\ \ \boxed{ \ \ \ \ x = 2.77777.... \ }$

-_______________

$\boxed{ \ \ \ 9x = 25 \ \ \ }$

$\boxed{ \ x = \frac{25}{9} \ }$

Therefore, the result is $\boxed{\boxed{ \ 2.\overline{7} = \frac{25}{9} \ }}$

Learn more

1. Find out the fraction of the space within the atom is occupied by the nucleus brainly.com/question/10818405
2. A repeating decimal brainly.com/question/1757979
3. ²/₇m - ¹/₇ = ³/₁₄ solve step by step brainly.com/question/4853649

Keywords: 2.77777..., repeating as fraction, decimals, number, repeat endlessly, infinitely, the division, the quotient, subtract, ²⁵/₉

Answer 2

To convert 2.77777777777 to a fraction:
Assume x = 2.7777777777......equation 1

Now, notice that the repeating digit is 7
 multiply both sides of the equation by 10:
10x = 27.7777777777.......equation 2

Subtract equation 1 from equation 2 as follows:
10x - x = 27.7777777777 - 2.7777777777
9x = 25
Therefore x = 25/9

Based on this, 2.7 repeated can be written as a fraction = 25/9