Sure, let's address the given problem step-by-step.
### Part (a): Convert [tex]\(2 \frac{5}{8}\)[/tex] to a decimal
To convert the mixed number [tex]\(2 \frac{5}{8}\)[/tex] to a decimal:
1. Understand that [tex]\(2 \frac{5}{8}\)[/tex] consists of a whole number part (2) and a fractional part [tex]\(\frac{5}{8}\)[/tex].
2. Convert the fractional part to a decimal:
- To convert [tex]\(\frac{5}{8}\)[/tex] to a decimal, divide the numerator (5) by the denominator (8).
- [tex]\(\frac{5}{8} = 0.625\)[/tex]
3. Add the decimal form of the fractional part to the whole number part:
- [tex]\(2 \frac{5}{8} = 2 + 0.625 = 2.625\)[/tex]
So, [tex]\(2 \frac{5}{8}\)[/tex] in decimal form is 2.625.
### Part (b): What was Ariel's likely error?
Ariel claimed that [tex]\(2 \frac{5}{8}\)[/tex] is the same as 2.58. Let's examine what mistake Ariel might have made:
- Ariel appears to have assumed that the fractional part of [tex]\(2 \frac{5}{8}\)[/tex], which is [tex]\(\frac{5}{8}\)[/tex], directly translates to 5/100 in decimal form without proper conversion.
- This indicates that Ariel likely thought that [tex]\(\frac{5}{8} \approx 0.58\)[/tex].
However, the correct decimal conversion of [tex]\(\frac{5}{8}\)[/tex] is 0.625, not 0.58. The decimal 0.58 is closer to [tex]\(\frac{58}{100}\)[/tex] or [tex]\(\frac{29}{50}\)[/tex], which is not equivalent to [tex]\(\frac{5}{8}\)[/tex].
Hence, Ariel likely confused the fractional conversion and prematurely considered [tex]\(\frac{5}{8}\)[/tex] as 0.58 instead of correctly calculating it as 0.625.
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### At a Grocery Store: Equation for Daniel
Let's address the initial part of the question fully before interpreting the second part of your statement which seems incomplete. Based on the context, if there is a specific question regarding Daniel and fractions, please provide the full details, and I'd be happy to help further!
