Let's determine how much money Bill has by converting the fraction [tex]\(\frac{19}{76}\)[/tex] into a decimal.
Step-by-Step Solution:
1. Understand the Fraction:
Bill's money is represented as a fraction of one dollar: [tex]\(\frac{19}{76}\)[/tex].
2. Simplify the Fraction (if possible):
- We check if the numerator (19) and the denominator (76) have a common factor.
- The greatest common divisor (GCD) of 19 and 76 is 19.
- When we divide both numerator and denominator by 19, we get:
[tex]\[
\frac{19 \div 19}{76 \div 19} = \frac{1}{4}
\][/tex]
3. Convert the Fraction to Decimal Form:
- Now, we convert [tex]\(\frac{1}{4}\)[/tex] to its decimal form:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
Hence, the decimal representation of [tex]\(\frac{19}{76}\)[/tex] is [tex]\(0.25\)[/tex].
Therefore, Bill has [tex]\(0.25\)[/tex] dollars, which is the same as 25 cents. Bill has 25 cents in total.
