To convert the decimal 3.25 into a fraction, we can follow these detailed steps:
1. Express the decimal as a mixed number:
The decimal 3.25 can be written as [tex]\( 3 + 0.25 \)[/tex].
2. Convert the decimal part to a fraction:
The decimal [tex]\( 0.25 \)[/tex] can be written as the fraction [tex]\( \frac{25}{100} \)[/tex].
3. Simplify the fraction:
- Both the numerator (25) and the denominator (100) have a common factor, which is 25.
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 25:
[tex]\[
\frac{25}{100} = \frac{25 \div 25}{100 \div 25} = \frac{1}{4}
\][/tex]
4. Combine the integer part with the simplified fractional part:
- We already have the whole number part as 3 and the simplified fractional part as [tex]\( \frac{1}{4} \)[/tex].
- Therefore, [tex]\( 3.25 \)[/tex] can be expressed as the mixed number [tex]\( 3 \frac{1}{4} \)[/tex].
5. Convert the mixed number to an improper fraction:
- To convert [tex]\( 3 \frac{1}{4} \)[/tex] into an improper fraction, multiply the whole number part by the denominator of the fractional part and add the numerator of the fractional part:
[tex]\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
\][/tex]
Therefore, the decimal [tex]\( 3.25 \)[/tex] can be converted into the improper fraction [tex]\( \frac{13}{4} \)[/tex].
