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
- Find out the fraction of the space within the atom is occupied by the nucleus https://brainly.com/question/10818405
- A repeating decimal https://brainly.com/question/1757979
- ²/₇m - ¹/₇ = ³/₁₄ solve step by step https://brainly.com/question/4853649
Keywords: 2.77777..., repeating as fraction, decimals, number, repeat endlessly, infinitely, the division, the quotient, subtract, ²⁵/₉
