Express 0.38 as a fraction in simplest form
The Correct Answer and Explanation is:
Answer:
0.38 as a fraction in simplest form is 19/50.
Explanation:
To express 0.38 as a fraction, we begin by recognizing that it is a decimal number. The digits “38” are in the hundredths place, meaning 0.38 is the same as 38 divided by 100. This gives us the fraction: 38100\frac{38}{100}10038
This fraction is not yet in its simplest form. To simplify it, we need to find the greatest common divisor (GCD) of the numerator (38) and the denominator (100). The GCD is the largest number that divides both numbers without leaving a remainder.
First, we find the factors of both numbers:
- Factors of 38 are: 1, 2, 19, 38
- Factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor shared by both is 2.
Now we divide both the numerator and the denominator by 2: 38÷2100÷2=1950\frac{38 ÷ 2}{100 ÷ 2} = \frac{19}{50}100÷238÷2=5019
Thus, the simplified fraction is: 1950\frac{19}{50}5019
This is the simplest form because 19 is a prime number, and it shares no common factors with 50 other than 1.
This process of converting a decimal to a fraction involves understanding place value. Because 0.38 terminates after two digits, it can always be written over 100. Not all decimals are this easy. Some repeating decimals require a different method, often involving algebra. However, for terminating decimals like 0.38, placing them over a power of ten (like 10, 100, or 1000) makes the conversion straightforward.
Finally, always remember to simplify your fraction by dividing both the numerator and the denominator by their greatest common factor. This ensures your final answer is in the simplest form, making it easier to interpret or use in further calculations.
