Express 0.23 as a fraction in its simplest form.
The Correct Answer and Explanation is :
To express ( 0.23 ) as a fraction in its simplest form, follow these steps:
Step 1: Recognize the Decimal Form
The decimal ( 0.23 ) represents the number 23 hundredths, which is written as:
[
0.23 = \frac{23}{100}
]
Step 2: Check for Simplification
The next step is to simplify the fraction ( \frac{23}{100} ). To do this, we need to find the greatest common divisor (GCD) of 23 and 100. The number 23 is a prime number, and since 100 does not have 23 as a factor, the greatest common divisor of 23 and 100 is 1.
Step 3: Simplify the Fraction
Because the GCD of 23 and 100 is 1, the fraction ( \frac{23}{100} ) is already in its simplest form. There are no common factors that can divide both the numerator (23) and the denominator (100) other than 1.
Step 4: Conclusion
Thus, ( 0.23 ) as a fraction in its simplest form is:
[
\frac{23}{100}
]
Explanation of the Process:
- Decimal to Fraction Conversion: To convert a decimal to a fraction, write the decimal number over a power of 10. The number of decimal places determines the power of 10. For example, 0.23 has two decimal places, so we place it over 100.
- Simplification: Simplifying a fraction involves finding the GCD of the numerator and the denominator and dividing both by that number. If the GCD is 1, the fraction is already in its simplest form.
- Prime Numbers: In this case, 23 is a prime number, meaning it only has divisors of 1 and 23. Since 100 is not divisible by 23, the fraction cannot be simplified further.
This approach shows the straightforward method of converting and simplifying decimals to fractions.