To express the number 2.41 as a rational number, follow these steps:
1. Recognize the Decimal Form: The number 2.41 can be broken down into its decimal components. Here, 2.41 means 2 plus 0.41.
2. Convert the Decimal to a Fraction: To convert 2.41 to a fraction, first consider the fractional part (0.41). The decimal 0.41 can be written as 41/100 because the decimal 41 is in the hundredths place.
3. Combine the Whole Number with the Fraction: Now, represent 2.41 as a single rational number.
[tex]\[
2 + 0.41 = 2 + \frac{41}{100}
\][/tex]
4. Convert the Whole Number to a Fraction: To easily combine the whole number and the fraction, convert the whole number 2 into a fraction by writing it as 200/100 (since 2 is equivalent to [tex]\(\frac{200}{100}\)[/tex] when considering the denominator of 100).
[tex]\[
2 = \frac{200}{100}
\][/tex]
5. Add the Fractions: Add the fractions with a common denominator.
[tex]\[
\frac{200}{100} + \frac{41}{100} = \frac{200 + 41}{100} = \frac{241}{100}
\][/tex]
So, the rational number that represents 2.41 is [tex]\(\frac{241}{100}\)[/tex].
6. Simplification Check: We should check if [tex]\(\frac{241}{100}\)[/tex] can be simplified. Since 241 is a prime number and 100 is 2² × 5², they have no common factors other than 1. Thus, [tex]\(\frac{241}{100}\)[/tex] is already in its simplest form.
Therefore, the simplest form of the rational number representing 2.41 is [tex]\( \frac{241}{100} \)[/tex].
