When expressed as a mixed number or fraction, 0.0075 is
The Correct Answer and Explanation is:
To express 0.0075 as a mixed number or fraction, we can follow these steps:
Step 1: Understanding the Decimal Value
The number 0.0075 represents a decimal where the digits are to the right of the decimal point. The value of 0.0075 can be broken down into a fraction by considering the place value of the digits:
- The first digit after the decimal point (0) is in the tenths place.
- The second digit (0) is in the hundredths place.
- The third digit (7) is in the thousandths place.
- The fourth digit (5) is in the ten-thousandths place.
Thus, 0.0075 is the same as 75 ten-thousandths, or 75/10,000.
Step 2: Simplifying the Fraction
Now, we need to simplify the fraction 75/10,000. To do this, we find the greatest common divisor (GCD) of 75 and 10,000.
- The factors of 75 are 1, 3, 5, 15, 25, 75.
- The factors of 10,000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 800, 1,000, 2,000, 5,000, 10,000.
The GCD of 75 and 10,000 is 25. We divide both the numerator and the denominator of the fraction by 25:
[
\frac{75 \div 25}{10,000 \div 25} = \frac{3}{400}
]
Thus, the fraction 75/10,000 simplifies to 3/400.
Step 3: Converting to a Mixed Number
Since the value is less than 1, 3/400 cannot be converted into a mixed number (which would require the fraction to be greater than 1). Therefore, the simplest fractional representation of 0.0075 is 3/400.
Final Answer:
0.0075 as a fraction is 3/400.