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Answer :
To find the fraction and percent equivalents of the decimal 0.84, let's go through the options and check which ones are correct:
1. Percent Equivalent:
- To convert a decimal to a percent, multiply by 100.
- For 0.84, [tex]\( 0.84 \times 100 = 84\% \)[/tex].
- So, option A ([tex]$84\%$[/tex]) is correct.
2. Fraction Equivalent:
- The decimal 0.84 can be written as the fraction [tex]\(\frac{84}{100}\)[/tex].
- Option B ([tex]$\frac{84}{100}$[/tex]) is presented, and this is correct.
However, fractions can often be simplified:
- [tex]\(\frac{84}{100}\)[/tex] simplifies by dividing both the numerator and denominator by their greatest common divisor, which is 4.
- This gives us [tex]\(\frac{84 \div 4}{100 \div 4} = \frac{21}{25}\)[/tex].
- So, the simplified fraction for 0.84 is [tex]\(\frac{21}{25}\)[/tex].
Now, let's examine the other options:
- Option C ([tex]$16\%$[/tex]): This is not correct because 0.84 is equivalent to [tex]\(84\%\)[/tex], not [tex]\(16\%\)[/tex].
- Option D ([tex]$8.4\%$[/tex]): This is also not correct, as the correct percentage for 0.84 is [tex]\(84\%\)[/tex].
- Option E ([tex]$\frac{80}{100}$[/tex]): This fraction is equivalent to 0.80, not 0.84, so this is incorrect.
- Option F ([tex]$\frac{16}{100}$[/tex]): This represents the decimal 0.16, not 0.84, so this is also incorrect.
In conclusion, the correct choices are:
- A. [tex]$84\%$[/tex]
- B. [tex]$\frac{84}{100}$[/tex] (which simplifies to [tex]$\frac{21}{25}$[/tex])
1. Percent Equivalent:
- To convert a decimal to a percent, multiply by 100.
- For 0.84, [tex]\( 0.84 \times 100 = 84\% \)[/tex].
- So, option A ([tex]$84\%$[/tex]) is correct.
2. Fraction Equivalent:
- The decimal 0.84 can be written as the fraction [tex]\(\frac{84}{100}\)[/tex].
- Option B ([tex]$\frac{84}{100}$[/tex]) is presented, and this is correct.
However, fractions can often be simplified:
- [tex]\(\frac{84}{100}\)[/tex] simplifies by dividing both the numerator and denominator by their greatest common divisor, which is 4.
- This gives us [tex]\(\frac{84 \div 4}{100 \div 4} = \frac{21}{25}\)[/tex].
- So, the simplified fraction for 0.84 is [tex]\(\frac{21}{25}\)[/tex].
Now, let's examine the other options:
- Option C ([tex]$16\%$[/tex]): This is not correct because 0.84 is equivalent to [tex]\(84\%\)[/tex], not [tex]\(16\%\)[/tex].
- Option D ([tex]$8.4\%$[/tex]): This is also not correct, as the correct percentage for 0.84 is [tex]\(84\%\)[/tex].
- Option E ([tex]$\frac{80}{100}$[/tex]): This fraction is equivalent to 0.80, not 0.84, so this is incorrect.
- Option F ([tex]$\frac{16}{100}$[/tex]): This represents the decimal 0.16, not 0.84, so this is also incorrect.
In conclusion, the correct choices are:
- A. [tex]$84\%$[/tex]
- B. [tex]$\frac{84}{100}$[/tex] (which simplifies to [tex]$\frac{21}{25}$[/tex])
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