Answer
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Step 1:I'll solve this problem step by step, following the LaTeX formatting guidelines precisely:
Step 2:: Identify the decimal
The decimal we want to convert is $$0.185
Step 3:: Multiply by a power of 10 to make it a whole number
0.185 \times 1000 = 185
To convert this decimal to a fraction, we'll multiply by a power of 10 that moves the decimal point to the right:
Step 4:: Set up the fraction
\frac{185}{1000}
Now we can write this as a fraction with 1000 as the denominator:
Step 5:: Simplify the fraction
To simplify, we'll find the greatest common divisor (GCD) of 185 and 1000: The factors of 185 are: 1, 5, 37, 185 The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000 The greatest common factor is 5
Step 6:: Divide both numerator and denominator by the GCD
\frac{185 \div 5}{1000 \div 5} = \frac{37}{200}
Final Answer
Key Insights: - This method works by multiplying the decimal by a power of 10 to convert it to a whole number - Always simplify the resulting fraction by dividing both numerator and denominator by their greatest common factor - The final fraction is equivalent to the original decimal
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