What is 3.375 written as a fraction in simplest form
The correct Answer and Explanation is:
To express 3.375 as a fraction in its simplest form, follow these steps:
Step 1: Express the decimal as a fraction.
The decimal 3.375 can be written as 33751000\frac{3375}{1000}10003375 since 3.375 has three digits after the decimal point, meaning it is equivalent to 3,375 over 1,000.
Step 2: Simplify the fraction.
Now, simplify the fraction by dividing both the numerator (3,375) and the denominator (1,000) by their greatest common divisor (GCD).
- First, find the GCD of 3,375 and 1,000. Both numbers are divisible by 125: 3375÷1251000÷125=278\frac{3375 \div 125}{1000 \div 125} = \frac{27}{8}1000÷1253375÷125=827
Step 3: Confirm the result.
Thus, 3.375 as a fraction in its simplest form is 278\frac{27}{8}827.
Explanation:
The process of converting a decimal into a fraction involves determining how many decimal places are present in the number. In the case of 3.375, there are three decimal places, meaning the decimal represents thousandths. This allows us to write 3.375 as 33751000\frac{3375}{1000}10003375.
Next, simplifying the fraction is important to ensure it is expressed in its lowest terms. Simplification involves finding the greatest common divisor (GCD), which is the largest number that can divide both the numerator and denominator evenly. By dividing 3,375 and 1,000 by their GCD (125), we reduce the fraction to 278\frac{27}{8}827.
It’s also important to note that 278\frac{27}{8}827 is an improper fraction because the numerator is larger than the denominator. If needed, this improper fraction can also be written as a mixed number:278=338\frac{27}{8} = 3 \frac{3}{8}827=383
This confirms that 3.375 is the decimal equivalent of the mixed number 3383 \frac{3}{8}383. Thus, 3.375 as a fraction is 278\frac{27}{8}827 in its simplest form.