Convert the decimal number 0.05 into a fraction in its lowest form.
The correct answer and explanation is:
Correct Answer:
0.05 = 1/20
Explanation:
To convert the decimal number 0.05 into a fraction in its lowest form, begin by understanding the place value of each digit in the decimal. The number 0.05 has two digits after the decimal point. The digit 5 is in the hundredths place, meaning that 0.05 can be written as:
0.05 = 5/100
This is a fraction, but it is not in its lowest terms. To simplify a fraction, divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). In this case, the GCD of 5 and 100 is 5.
Now, divide both parts of the fraction by 5:
5 ÷ 5 = 1
100 ÷ 5 = 20
This simplifies the fraction:
5/100 = 1/20
So, 0.05 as a fraction in its simplest form is 1/20.
Converting decimals into fractions helps to understand the relationships between different kinds of numbers. It also allows for easier comparison and computation in some mathematical problems. For example, in problems involving percentages, ratios, or proportions, working with fractions can often make the operations more straightforward.
Decimals like 0.05 are especially easy to convert because they terminate (they do not go on forever). The method is to recognize the decimal place value and then simplify the resulting fraction. In the case of 0.05, the decimal ends after two digits, indicating it is in the hundredths place. After writing it as 5/100, simplifying gives the clean, final answer.
Understanding this conversion builds a foundation for more complex topics in mathematics, such as algebra and number theory.