Which of the following is equivalent to 2.76?

A. [tex]\(2.76 \%\)[/tex]
B. [tex]\(27.6 \%\)[/tex]
C. [tex]\(2 \frac{19}{25}\)[/tex]
D. [tex]\(\frac{25}{19}\)[/tex]



Answer :

Sure, let's analyze each of the given options to see which one is equivalent to 2.76.

1. [tex]$2.76 \%$[/tex]:
To convert a percentage to a decimal, you divide by 100. Therefore,
[tex]\[ 2.76\% = \frac{2.76}{100} = 0.0276 \][/tex]
This is not equivalent to 2.76.

2. [tex]$27.6 \%$[/tex]:
Similarly, convert this percentage to a decimal by dividing by 100.
[tex]\[ 27.6\% = \frac{27.6}{100} = 0.276 \][/tex]
This is also not equivalent to 2.76.

3. [tex]$2 \frac{19}{25}$[/tex]:
Convert this mixed number to an improper fraction and then to a decimal.
[tex]\[ 2 + \frac{19}{25} \][/tex]
To convert [tex]\( \frac{19}{25} \)[/tex] to a decimal, you perform the division:
[tex]\[ \frac{19}{25} = 0.76 \][/tex]
Adding this to 2:
[tex]\[ 2 + 0.76 = 2.76 \][/tex]
This is indeed equivalent to 2.76.

4. [tex]$\frac{25}{19}$[/tex]:
Convert this fraction to a decimal by performing the division.
[tex]\[ \frac{25}{19} \approx 1.3157894736842106 \][/tex]
This is not equivalent to 2.76.

From these steps, the only option equivalent to 2.76 is:
[tex]\[ 2 \frac{19}{25} \][/tex]