Question

convert the following decimals into fractions.
0.075 = \\(\frac{92}{25}\\)
3.68 =

Explanation:

Step1: Analyze the decimal 3.68

3.68 can be written as a mixed number or an improper fraction. First, consider the decimal part 0.68.

Step2: Convert 0.68 to fraction

0.68 is 68 hundredths, so it can be written as $\frac{68}{100}$. Then simplify this fraction by dividing numerator and denominator by 4: $\frac{68\div4}{100\div4}=\frac{17}{25}$.

Step3: Combine with the whole number part

The whole number part is 3, so as a mixed number, 3.68 is $3\frac{17}{25}$. To convert to an improper fraction, multiply the whole number (3) by the denominator of the fraction part (25) and add the numerator (17): $3\times25 + 17=75 + 17 = 92$. So the improper fraction is $\frac{92}{25}$. Wait, but let's check the first decimal 0.075. Wait, maybe there was a mistake in the first one, but let's focus on 3.68. Wait, 3.68: 3 is the whole number, 0.68 = $\frac{68}{100}=\frac{17}{25}$. Then 3 = $\frac{75}{25}$, so $\frac{75}{25}+\frac{17}{25}=\frac{92}{25}$. But for 0.075: 0.075 is 75 thousandths, so $\frac{75}{1000}=\frac{3}{40}$ (dividing numerator and denominator by 25: 75÷25=3, 1000÷25=40). But the problem shows 0.075 equal to $\frac{92}{25}$ which is wrong, but let's solve 3.68. So 3.68: 3 + 0.68 = 3 + $\frac{68}{100}$ = 3 + $\frac{17}{25}$ = $\frac{75 + 17}{25}$ = $\frac{92}{25}$. Wait, maybe the first one was a typo, but for 3.68, the conversion is as follows.

Answer:

$\frac{92}{25}$ (or $3\frac{17}{25}$)