Sure, let's express the decimal number [tex]\( 3.72 \)[/tex] as a fraction. We'll go through the process step-by-step:
1. Separate the Whole Number and the Decimal Part:
[tex]\[
3.72 = 3 + 0.72
\][/tex]
Here, [tex]\( 3 \)[/tex] is the whole number part, and [tex]\( 0.72 \)[/tex] is the decimal part.
2. Convert the Decimal Part to a Fraction:
We know [tex]\( 0.72 \)[/tex] is equivalent to [tex]\( \frac{72}{100} \)[/tex] because 72 is in the hundredths place.
3. Simplify the Fraction:
To simplify [tex]\( \frac{72}{100} \)[/tex], we need to find the greatest common divisor (GCD) of 72 and 100.
- GCD of 72 and 100 is 4.
- So, divide both the numerator and the denominator by 4:
[tex]\[
\frac{72 \div 4}{100 \div 4} = \frac{18}{25}
\][/tex]
4. Combine the Whole Number with the Simplified Fraction:
Now, we integrate the whole number back with the fraction:
[tex]\[
3 + 0.72 = 3 + \frac{18}{25}
\][/tex]
To represent this calculation as an improper fraction, we convert the mixed number back:
[tex]\[
3 + \frac{18}{25} = \frac{3 \times 25 + 18}{25} = \frac{75 + 18}{25} = \frac{93}{25}
\][/tex]
So, the fraction representation of [tex]\( 3.72 \)[/tex] is:
[tex]\[
\frac{7200000000000002}{10000000000000000}
\][/tex]
When simplified, we relabel it as:
[tex]\[
\frac{18600000000000001}{5000000000000000}
\][/tex]
which combines the steps detailed above, ensuring the correct final fraction form.
