Let's determine which of the given decimals or fractions is equivalent to neither 0.825 nor [tex]\(\frac{5}{8}\)[/tex].
First, we need to consider the values 0.825 and [tex]\(\frac{5}{8}\)[/tex]:
1. 0.825
2. [tex]\(\frac{5}{8}\)[/tex]
To identify if the fractions are equivalent to these values, let's convert 0.825 and [tex]\(\frac{5}{8}\)[/tex] into decimals:
1. We already have 0.825 as a decimal.
2. Convert [tex]\(\frac{5}{8}\)[/tex] to decimal:
[tex]\[
\frac{5}{8} = 5 \div 8 = 0.625
\][/tex]
We should identify the value among the given options that is neither 0.825 nor 0.625.
Now let's go through each option:
1. 0.85
- This value is neither 0.825 nor 0.625.
2. [tex]\(\frac{10}{16}\)[/tex]
- Convert [tex]\(\frac{10}{16}\)[/tex] to a decimal:
[tex]\[
\frac{10}{16} = 10 \div 16 = 0.625
\][/tex]
- This value is equivalent to 0.625, which is the decimal representation of [tex]\(\frac{5}{8}\)[/tex].
3. [tex]\(\frac{33}{40}\)[/tex]
- Convert [tex]\(\frac{33}{40}\)[/tex] to a decimal:
[tex]\[
\frac{33}{40} = 33 \div 40 = 0.825
\][/tex]
- This value is equivalent to 0.825.
4. 0.625
- This value is already given as 0.625, which is the decimal representation of [tex]\(\frac{5}{8}\)[/tex].
After converting all the given values, we can see:
- 0.85 is neither 0.825 nor 0.625.
- [tex]\(\frac{10}{16} = 0.625\)[/tex].
- [tex]\(\frac{33}{40} = 0.825\)[/tex].
- 0.625 is 0.625.
Hence, the value that is neither 0.825 nor [tex]\(\frac{5}{8}\)[/tex] is:
[tex]\[ \boxed{0.85} \][/tex]
