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Sagot :
Answer:
[tex]\(\frac{8}{3}\).[/tex]
Step-by-step explanation:
To convert [tex]\(2.\overline{6}\) (2.66666...)[/tex] to a fraction, follow these steps:
1. Let [tex]\( x = 2.\overline{6} \).[/tex]
2. Multiply both sides by [tex]10: \( 10x = 26.\overline{6} \).[/tex]
3. Subtract the original equation from this new equation:
[tex]\[ 10x - x = 26.\overline{6} - 2.\overline{6} \][/tex]
[tex]\[ 9x = 24 \][/tex]
4. Solve for [tex]\( x \):[/tex]
[tex]\[ x = \frac{24}{9} \][/tex]
5. Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor (3):
[tex]\[ x = \frac{24 \div 3}{9 \div 3} = \frac{8}{3} \][/tex]
Therefore, [tex]\(2.\overline{6}\)[/tex] as a simplified fraction is [tex]\(\frac{8}{3}\).[/tex]
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