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Answer :
- Convert the percentage to a decimal: $740\% = \frac{740}{100} = 7.4$.
- Convert the percentage to a fraction: $740\% = \frac{740}{100}$.
- Simplify the fraction: $\frac{740}{100} = \frac{37}{5}$.
- Convert the improper fraction to a mixed number: $\frac{37}{5} = 7 \frac{2}{5}$. The answer is $\boxed{7.4 \text{ and } 7 \frac{2}{5}}$.
### Explanation
1. Converting Percentage to Decimal
We need to convert $740\%$ into a decimal and a mixed number. First, let's convert the percentage to a decimal. To do this, we divide the percentage by 100.
2. Decimal Representation
$740\% = \frac{740}{100} = 7.4$. So, the decimal representation of $740\%$ is 7.4.
3. Converting Percentage to Fraction
Now, let's convert $740\%$ to a mixed number. We already know that $740\% = \frac{740}{100}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20.
4. Simplifying the Fraction
$\frac{740}{100} = \frac{740 \div 20}{100 \div 20} = \frac{37}{5}$. Now, we convert the improper fraction $\frac{37}{5}$ to a mixed number. To do this, we divide 37 by 5.
5. Mixed Number Representation
$37 \div 5 = 7$ with a remainder of 2. So, $\frac{37}{5} = 7 \frac{2}{5}$. Therefore, the mixed number representation of $740\%$ is $7 \frac{2}{5}$.
6. Final Answer
Thus, $740\%$ as a decimal is 7.4 and as a mixed number is $7 \frac{2}{5}$.
### Examples
In finance, if an investment yields a return of 740%, it means the investment has grown 7.4 times its original value. Expressing this as a mixed number, $7 \frac{2}{5}$, helps to visualize the substantial growth beyond the initial investment. This kind of calculation is useful for understanding the magnitude of returns in investments, business growth, or any situation involving percentage increases.
- Convert the percentage to a fraction: $740\% = \frac{740}{100}$.
- Simplify the fraction: $\frac{740}{100} = \frac{37}{5}$.
- Convert the improper fraction to a mixed number: $\frac{37}{5} = 7 \frac{2}{5}$. The answer is $\boxed{7.4 \text{ and } 7 \frac{2}{5}}$.
### Explanation
1. Converting Percentage to Decimal
We need to convert $740\%$ into a decimal and a mixed number. First, let's convert the percentage to a decimal. To do this, we divide the percentage by 100.
2. Decimal Representation
$740\% = \frac{740}{100} = 7.4$. So, the decimal representation of $740\%$ is 7.4.
3. Converting Percentage to Fraction
Now, let's convert $740\%$ to a mixed number. We already know that $740\% = \frac{740}{100}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 20.
4. Simplifying the Fraction
$\frac{740}{100} = \frac{740 \div 20}{100 \div 20} = \frac{37}{5}$. Now, we convert the improper fraction $\frac{37}{5}$ to a mixed number. To do this, we divide 37 by 5.
5. Mixed Number Representation
$37 \div 5 = 7$ with a remainder of 2. So, $\frac{37}{5} = 7 \frac{2}{5}$. Therefore, the mixed number representation of $740\%$ is $7 \frac{2}{5}$.
6. Final Answer
Thus, $740\%$ as a decimal is 7.4 and as a mixed number is $7 \frac{2}{5}$.
### Examples
In finance, if an investment yields a return of 740%, it means the investment has grown 7.4 times its original value. Expressing this as a mixed number, $7 \frac{2}{5}$, helps to visualize the substantial growth beyond the initial investment. This kind of calculation is useful for understanding the magnitude of returns in investments, business growth, or any situation involving percentage increases.
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