What is 0.07 as a fraction in simplest form?
The Correct Answer and Explanation is:
To express 0.07 as a fraction in its simplest form, we follow a step-by-step process:
Step 1: Express 0.07 as a fraction
The decimal 0.07 is equivalent to 7 hundredths. This is because the two digits after the decimal point indicate that the value is in the hundredths place. So, we can write 0.07 as:
[
0.07 = \frac{7}{100}
]
Step 2: Check if the fraction can be simplified
The next step is to check if the fraction (\frac{7}{100}) can be simplified further. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (7) and the denominator (100).
- The factors of 7 are: 1, 7.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
The greatest common divisor (GCD) of 7 and 100 is 1 because they have no other common factors except 1.
Since the GCD is 1, the fraction is already in its simplest form. Therefore, the fraction (\frac{7}{100}) cannot be simplified any further.
Final Answer:
The decimal 0.07 as a fraction in simplest form is:
[
\frac{7}{100}
]
Explanation:
A fraction represents a part of a whole. When a decimal is converted into a fraction, the number of digits to the right of the decimal point determines the denominator. In the case of 0.07, the decimal places extend two digits, meaning the denominator is 100 (as 100 is the place value for hundredths). The number 7 in the hundredths place becomes the numerator.
Because 7 and 100 have no common divisors other than 1, the fraction is already in its simplest form. This process of converting decimals to fractions and simplifying them is essential in mathematical operations, especially when performing addition, subtraction, or multiplication with fractions.