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Answer :
Sure! Let's convert [tex]\( 740\% \)[/tex] into both a decimal and a mixed number.
### Converting Percentage to Decimal
To convert a percentage to a decimal, you divide by 100.
[tex]\[ 740\% = \frac{740}{100} = 7.4 \][/tex]
So, [tex]\( 740\% \)[/tex] as a decimal is [tex]\( 7.4 \)[/tex].
### Converting Decimal to a Mixed Number
Next, we need to convert [tex]\( 7.4 \)[/tex] into a mixed number.
1. Split [tex]\( 7.4 \)[/tex] into its integer and fractional parts:
- Integer part: [tex]\( 7 \)[/tex]
- Fractional part: [tex]\( 0.4 \)[/tex]
2. Convert the fractional part [tex]\( 0.4 \)[/tex] into a fraction:
[tex]\[
0.4 = \frac{4}{10}
\][/tex]
3. Simplify the fraction [tex]\(\frac{4}{10}\)[/tex]:
- Both 4 and 10 can be divided by their greatest common divisor (GCD), which is 2.
[tex]\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\][/tex]
So, [tex]\( 0.4 \)[/tex] simplifies to [tex]\( \frac{2}{5} \)[/tex].
4. Combine the integer part and the simplified fraction to get the mixed number:
[tex]\[
7.4 = 7 \frac{2}{5}
\][/tex]
Therefore, [tex]\( 740\% \)[/tex] as a mixed number is [tex]\( 7 \frac{2}{5} \)[/tex].
### Conclusion
- [tex]\( 740\% \)[/tex] as a decimal is [tex]\( 7.4 \)[/tex].
- [tex]\( 740\% \)[/tex] as a mixed number is [tex]\( 7 \frac{2}{5} \)[/tex].
Among the given choices, the correct answer is:
```
7.4 and [tex]\( 7 \frac{2}{5} \)[/tex]
```
### Converting Percentage to Decimal
To convert a percentage to a decimal, you divide by 100.
[tex]\[ 740\% = \frac{740}{100} = 7.4 \][/tex]
So, [tex]\( 740\% \)[/tex] as a decimal is [tex]\( 7.4 \)[/tex].
### Converting Decimal to a Mixed Number
Next, we need to convert [tex]\( 7.4 \)[/tex] into a mixed number.
1. Split [tex]\( 7.4 \)[/tex] into its integer and fractional parts:
- Integer part: [tex]\( 7 \)[/tex]
- Fractional part: [tex]\( 0.4 \)[/tex]
2. Convert the fractional part [tex]\( 0.4 \)[/tex] into a fraction:
[tex]\[
0.4 = \frac{4}{10}
\][/tex]
3. Simplify the fraction [tex]\(\frac{4}{10}\)[/tex]:
- Both 4 and 10 can be divided by their greatest common divisor (GCD), which is 2.
[tex]\[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
\][/tex]
So, [tex]\( 0.4 \)[/tex] simplifies to [tex]\( \frac{2}{5} \)[/tex].
4. Combine the integer part and the simplified fraction to get the mixed number:
[tex]\[
7.4 = 7 \frac{2}{5}
\][/tex]
Therefore, [tex]\( 740\% \)[/tex] as a mixed number is [tex]\( 7 \frac{2}{5} \)[/tex].
### Conclusion
- [tex]\( 740\% \)[/tex] as a decimal is [tex]\( 7.4 \)[/tex].
- [tex]\( 740\% \)[/tex] as a mixed number is [tex]\( 7 \frac{2}{5} \)[/tex].
Among the given choices, the correct answer is:
```
7.4 and [tex]\( 7 \frac{2}{5} \)[/tex]
```
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