To solve the problem involving the mixed number [tex]\( 2 \frac{45}{43} \)[/tex], we need to convert this mixed number into an improper fraction and then express it as a decimal.
1. Identify the parts of the mixed number:
- Whole part = 2
- Numerator of the fractional part = 45
- Denominator of the fractional part = 43
2. Convert the mixed number to an improper fraction:
To do this, we use the formula:
[tex]\[
\text{Improper fraction numerator} = (\text{Whole part} \times \text{Denominator}) + \text{Numerator}
\][/tex]
Plugging in the values:
[tex]\[
\text{Improper fraction numerator} = (2 \times 43) + 45 = 86 + 45 = 131
\][/tex]
3. The improper fraction is then:
[tex]\[
\frac{131}{43}
\][/tex]
4. Convert the improper fraction to a decimal:
To find the decimal form, divide the numerator by the denominator:
[tex]\[
\frac{131}{43} \approx 3.046511627906977
\][/tex]
Therefore, the final result is:
- Improper fraction: [tex]\(\frac{131}{43}\)[/tex]
- Decimal form: [tex]\(\approx 3.046511627906977\)[/tex]
