Answer :
To convert the decimal [tex]\(2.33\)[/tex] to a mixed number in simplest form, follow these steps:
1. Express the decimal as a fraction:
[tex]\[ 2.33 = \frac{233}{100} \][/tex]
This tells us that [tex]\(2.33\)[/tex] is equivalent to [tex]\(\frac{233}{100}\)[/tex].
2. Simplify the fraction, if possible:
To simplify [tex]\(\frac{233}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 233 and 100. The GCD of 233 and 100 is 1 because 233 is a prime number.
Since the GCD is 1, the fraction [tex]\(\frac{233}{100}\)[/tex] is already in its simplest form.
3. Convert to a mixed number:
Next, we consider the division of 233 by 100:
- The whole number part is the quotient of [tex]\(233 \div 100\)[/tex], which is 2.
- The fractional part is the remainder over the denominator. The remainder from the division [tex]\(233 \div 100\)[/tex] is 33.
So, we have:
[tex]\[ 2.33 = 2 + \frac{33}{100} \][/tex]
Thus, the mixed number form is:
[tex]\[ 2 \frac{33}{100} \][/tex]
Given the provided options, none match the correct mixed number. However, the correct decomposition indicates the conversion process. For a better match from your options, choice A) [tex]$233 / 100$[/tex] correctly represents the improper fraction form before converting to a mixed number.
As per the provided options:
- The closest would be:
[tex]\[ A) \frac{233}{100} \][/tex]
1. Express the decimal as a fraction:
[tex]\[ 2.33 = \frac{233}{100} \][/tex]
This tells us that [tex]\(2.33\)[/tex] is equivalent to [tex]\(\frac{233}{100}\)[/tex].
2. Simplify the fraction, if possible:
To simplify [tex]\(\frac{233}{100}\)[/tex], we need to find the greatest common divisor (GCD) of 233 and 100. The GCD of 233 and 100 is 1 because 233 is a prime number.
Since the GCD is 1, the fraction [tex]\(\frac{233}{100}\)[/tex] is already in its simplest form.
3. Convert to a mixed number:
Next, we consider the division of 233 by 100:
- The whole number part is the quotient of [tex]\(233 \div 100\)[/tex], which is 2.
- The fractional part is the remainder over the denominator. The remainder from the division [tex]\(233 \div 100\)[/tex] is 33.
So, we have:
[tex]\[ 2.33 = 2 + \frac{33}{100} \][/tex]
Thus, the mixed number form is:
[tex]\[ 2 \frac{33}{100} \][/tex]
Given the provided options, none match the correct mixed number. However, the correct decomposition indicates the conversion process. For a better match from your options, choice A) [tex]$233 / 100$[/tex] correctly represents the improper fraction form before converting to a mixed number.
As per the provided options:
- The closest would be:
[tex]\[ A) \frac{233}{100} \][/tex]
