What is 2.33 written as a mixed number in simplest form?
The correct answer and explanation is:
Correct Answer:
2.33 written as a mixed number in simplest form is 2 33/100.
Explanation (300 words):
To convert a decimal like 2.33 into a mixed number, you follow a step-by-step process that separates the whole number and converts the decimal portion into a fraction.
Step 1: Separate the whole number from the decimal.
In 2.33, the whole number is 2. That means the number is more than 2 but less than 3.
Step 2: Convert the decimal part (0.33) into a fraction.
The decimal 0.33 means 33 hundredths, which is written as: 0.33=331000.33 = \frac{33}{100}
Step 3: Simplify the fraction if possible.
Check if the fraction 33100\frac{33}{100} can be reduced. Look for any common factor between the numerator and the denominator.
- Factors of 33: 1, 3, 11, 33
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
Since the only common factor is 1, the fraction is already in simplest form.
Step 4: Combine the whole number with the simplified fraction.
Now put the whole number and the fraction together: 2+33100=2331002 + \frac{33}{100} = 2 \frac{33}{100}
So, 2.33 as a mixed number in simplest form is: 233100\boxed{2 \frac{33}{100}}
Extra Tip:
Sometimes, decimals like 0.333… (repeating) are mistaken for 0.33 (terminating). It’s important to distinguish them:
- 0.33 is exactly 33/100
- 0.333… (with repeating 3s) is equal to 1/3
But in this case, since the number is 2.33 (not repeating), the accurate fraction is 33/100, not 1/3.
This method is useful for interpreting decimals in everyday scenarios like money, measurements, and test scores where fractions are preferred.