a) Convert $$ 13 \frac{1}{8} $$ to a decimal. Rounded to the nearest hundredth. b) Would it be appropriate to use the decimal answer in part a to do further calculations, such as multiply $$ 13 \frac{7}{8} $$ by 18 ? No, it would not be appropriate. Yes, it would be appropriate. Convert $$ 14 \frac{3}{5} $$ to a decimal. Rounded to the nearest hundredth. d) Would it be appropriate to use the decimal answer in part c to do further calculations, such as multiply $$ 14 \frac{3}{5} $$ by 17 ? No, it would not be appropriate. Yes, it would be appropriate.

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**a) Converting $$ 13\frac{1}{8} $$ to a decimal (rounded to the nearest hundredth):**  
- Write the mixed number as the sum of its whole part and its fractional part:  
  $$
  13\frac{1}{8} = 13 + \frac{1}{8}.
  $$
- Convert the fraction to a decimal:  
  $$
  \frac{1}{8} = 0.125.
  $$  
- Add the whole number:  
  $$
  13 + 0.125 = 13.125.
  $$
- Round to the nearest hundredth:  
  The hundredths place is the second digit after the decimal point. In $$ 13.125 $$, the hundredths digit is $$ 2 $$ and the thousandths digit is $$ 5 $$. Since $$ 5 \geq 5 $$, we round the $$ 2 $$ up to $$ 3 $$.  
  Thus, $$ 13.125 $$ rounds to:  
  $$
  13.13.
  $$

**b) Appropriateness of using the decimal answer from part a for further calculations:**  
The decimal $$ 13.13 $$ is a rounded approximation of $$ 13\frac{1}{8} $$. Using rounded decimals in further calculations (such as multiplying $$ 13\frac{7}{8} $$ by 18) can introduce rounding errors. Therefore, it is generally not appropriate to use a rounded decimal when exact values are required for further calculations.  
$$
\textbf{Answer: No, it would not be appropriate.}
$$

**c) Converting $$ 14\frac{3}{5} $$ to a decimal (rounded to the nearest hundredth):**  
- Express the mixed number as:  
  $$
  14\frac{3}{5} = 14 + \frac{3}{5}.
  $$
- Convert the fraction to a decimal:  
  $$
  \frac{3}{5} = 0.6.
  $$
- Add the whole number:  
  $$
  14 + 0.6 = 14.6.
  $$
- Rounding $$ 14.6 $$ to the nearest hundredth:  
  Since $$ 0.6 $$ is equivalent to $$ 0.60 $$, we have:  
  $$
  14.60.
  $$

**d) Appropriateness of using the decimal answer from part c for further calculations:**  
In this case, the conversion $$ \frac{3}{5} = 0.6 $$ yields an exact decimal representation. Since $$ 14\frac{3}{5} $$ is exactly $$ 14.6 $$, there is no loss in precision. Therefore, it is appropriate to use $$ 14.6 $$ in further calculations, such as multiplying by 17.  
$$
\textbf{Answer: Yes, it would be appropriate.}
$$
a) $$ 13\frac{1}{8} = 13.13 $$ when rounded to the nearest hundredth. b) No, it would not be appropriate to use the decimal $$ 13.13 $$ for further calculations like multiplying $$ 13\frac{7}{8} $$ by 18. c) $$ 14\frac{3}{5} = 14.60 $$ when rounded to the nearest hundredth. d) Yes, it would be appropriate to use the decimal $$ 14.60 $$ for further calculations like multiplying $$ 14\frac{3}{5} $$ by 17.

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