1.666 non terminating decimal to fraction with solution
Answer (1)
To convert the non-terminating decimal 1.666... (where 6 repeats indefinitely) to a fraction, follow these steps:1. Let x be the repeating decimal: [tex]x = 1.666...[/tex]2. Multiply x by 10 to shift the decimal point:[tex]10x = 16.666...[/tex]3. Subtract the original equation from this new equation to eliminate the repeating part. [tex]10x - x = 16.666... - 1.666...[/tex][tex]9x = 15[/tex]4. Solve for x: [tex]x = \frac{15}{9} [/tex]5. Simplify the fraction: - Find the greatest common divisor (GCD) of 15 and 9, which is 3. - Divide both the numerator and the denominator by 3:[tex] \frac{15 \div 3}{9 \div 3} = \frac{5}{3} [/tex]So, the repeating decimal 1.666... can be expressed as the fraction [tex] \frac{15}{9} [/tex]CARRY ON LEARNING!
