To convert the mixed number [tex]\( 2 \frac{3}{16} \)[/tex] to a percent, follow these steps:
### Step 1: Convert the mixed number to an improper fraction
A mixed number consists of a whole number and a fractional part. In this case, the mixed number is [tex]\( 2 \frac{3}{16} \)[/tex], where 2 is the whole number, and [tex]\(\frac{3}{16}\)[/tex] is the fractional part.
To convert this to an improper fraction:
[tex]\[ \text{Improper fraction} = \text{Whole number} + \text{Fractional part} \][/tex]
[tex]\[ 2 \frac{3}{16} = 2 + \frac{3}{16} \][/tex]
### Step 2: Add the fractional part to the whole number
To add [tex]\(2\)[/tex] and [tex]\(\frac{3}{16}\)[/tex], we can express [tex]\(2\)[/tex] as a fraction with the same denominator:
[tex]\[ 2 = \frac{32}{16} \][/tex]
Now, add [tex]\(\frac{32}{16}\)[/tex] and [tex]\(\frac{3}{16}\)[/tex]:
[tex]\[ \frac{32}{16} + \frac{3}{16} = \frac{32 + 3}{16} = \frac{35}{16} \][/tex]
### Step 3: Convert the improper fraction to a decimal
To convert the improper fraction [tex]\(\frac{35}{16}\)[/tex] to a decimal, perform the division [tex]\(35 \div 16\)[/tex]:
[tex]\[ \frac{35}{16} \approx 2.1875 \][/tex]
### Step 4: Convert the decimal to a percent
To convert a decimal to a percent, multiply the decimal by [tex]\(100\)[/tex]:
[tex]\[ 2.1875 \times 100 = 218.75 \][/tex]
### Step 5: Round the percent to the nearest tenth
To round [tex]\(218.75\)[/tex] to the nearest tenth, look at the hundredths place (which is 5 in this case). Since it is 5 or greater, we round the tenths place up:
[tex]\[ 218.75 \approx 218.8 \][/tex]
### Final Answer
The mixed number [tex]\(2 \frac{3}{16}\)[/tex] converted to a percent is:
[tex]\[ \boxed{218.8\%} \][/tex]
