To express the decimal 0.00390625 as a fraction, we need to analyze its structure. This decimal has six decimal places, which means it can be represented over 1,000,000 (since 10^6 = 1,000,000).
Thus, we can write:
0.00390625 = \\frac{0.00390625}{1} = \\frac{0.00390625 imes 1,000,000}{1 imes 1,000,000} = \\frac{3,906.25}{1,000,000}
Next, to eliminate the decimal in the numerator, we multiply both the numerator and denominator by 100, leading to:
\\frac{3,906.25 \times 100}{1,000,000 \times 100} = \\frac{390625}{100000000}.
Now, we need to simplify this fraction by finding the greatest common divisor (GCD) of 390625 and 100000000. The GCD is 15625:
So, dividing both the numerator and denominator by 15625 gives:
\\frac{390625 \div 15625}{100000000 \div 15625} = \\frac{25}{6400}.
This fraction can be further simplified by recognizing that both 25 and 6400 can be divided by 25, resulting in:
\\frac{25 \div 25}{6400 \div 25} = \\frac{1}{256}.
Therefore, the decimal 0.00390625 can be expressed as the fraction:
\\frac{1}{256}.