Write 0.33 as a fraction in simplest form
The Correct Answer and Explanation is :
To convert the decimal 0.33 into a fraction in its simplest form, follow these steps:
- Understanding the Decimal: The decimal 0.33 can be expressed as 33 hundredths, which is represented mathematically as ( \frac{33}{100} ).
- Simplifying the Fraction: To simplify ( \frac{33}{100} ), we need to find the greatest common divisor (GCD) of the numerator (33) and the denominator (100).
- Finding the GCD:
- The factors of 33 are: 1, 3, 11, and 33.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, and 100.
- The common factors of 33 and 100 are: 1. Since the only common factor is 1, the GCD of 33 and 100 is 1. This means ( \frac{33}{100} ) is already in its simplest form.
- Final Answer: Thus, the fraction representation of 0.33 in simplest form is:
[
\frac{33}{100}
]
Explanation
Decimals represent parts of a whole, where the position of each digit conveys its value. In the case of 0.33, the digit ‘3’ is in the hundredths place, indicating that it represents 33 parts out of 100.
To express this as a fraction, you take the decimal number, recognize the place value, and construct the fraction by using the appropriate power of 10 as the denominator. Here, since 0.33 has two digits after the decimal, the denominator is 100.
After establishing the fraction, the next step is to simplify it. This process involves dividing both the numerator and the denominator by their GCD. Since the GCD here is 1, the fraction cannot be simplified further.
Understanding how to convert decimals to fractions is useful in many practical applications, from financial calculations to measurements in science. The ability to simplify fractions is equally important, as it helps in expressing values more clearly and facilitates easier mathematical operations. Thus, ( \frac{33}{100} ) is the simplest fractional form of 0.33.