To convert the decimal number 9.75 into a fraction, let's break down the steps carefully.
1. Understand the Decimal: The decimal number given is 9.75, which can be interpreted as [tex]\( 9 + 0.75 \)[/tex].
2. Convert the Fractional Part: The fractional part, 0.75, can be written as a fraction. To convert 0.75 to a fraction, recognize that it is equivalent to [tex]\(\frac{75}{100}\)[/tex].
3. Simplify the Fraction: The fraction [tex]\(\frac{75}{100}\)[/tex] can be simplified by finding the greatest common divisor (GCD) of 75 and 100, which is 25. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{75 \div 25}{100 \div 25} = \frac{3}{4}
\][/tex]
So, 0.75 as a fraction is [tex]\(\frac{3}{4}\)[/tex].
4. Combine the Whole and Fractional Parts: Now, combine the whole number part (9) and the fractional part ([tex]\(\frac{3}{4}\)[/tex]).
[tex]\[
9 + \frac{3}{4} = \frac{9 \times 4 + 3}{4} = \frac{36 + 3}{4} = \frac{39}{4}
\][/tex]
5. Result: Therefore, the decimal number 9.75 can be expressed as the fraction [tex]\(\frac{39}{4}\)[/tex].
Thus, the fraction form of 9.75 is [tex]\(\frac{39}{4}\)[/tex] with a numerator of 39 and a denominator of 4.
