Convert the following percents into fractions in the lowest form

Convert the following percents into fractions in the lowest form: 33 1/3%.

The Correct Answer and Explanation is:

To convert 33 1/3% into a fraction in lowest terms:

Step-by-step conversion:

1. Understand what percent means
   Percent means “per hundred.” So, 33 1/3% means 33 1/3 out of 100, or 3313%=331310033 \frac{1}{3}\% = \frac{33 \frac{1}{3}}{100}3331​%=1003331​​
2. Convert the mixed number to an improper fraction
   Convert 33 1/3 to an improper fraction: 3313=100333 \frac{1}{3} = \frac{100}{3}3331​=3100​
3. Divide by 100
   Now, divide this by 100 to convert it to a fraction: 1003÷100=1003×1100=100300\frac{100}{3} \div 100 = \frac{100}{3} \times \frac{1}{100} = \frac{100}{300}3100​÷100=3100​×1001​=300100​
4. Simplify the fraction
   Simplify 100/300 by dividing the numerator and denominator by 100: 100300=13\frac{100}{300} = \frac{1}{3}300100​=31​

✅ Final Answer:

13\boxed{\frac{1}{3}}31​​

📘 Explanation

When converting percentages to fractions, the goal is to express the percent as a part of one whole. Percent literally means “per hundred,” so any percent can be written as a fraction with 100 as the denominator. For example, 50% is equal to 50 out of 100, or 50/100, which simplifies to 1/2.

In this case, you are given 33 1/3%, which is a mixed number. First, convert this mixed number to an improper fraction. To do this, multiply the whole number part (33) by the denominator of the fractional part (3), giving 99. Then add the numerator (1), which gives 100. So, 33 1/3 becomes 100/3.

Since it is a percent, you need to divide this by 100 to get a fraction of a whole number. Dividing by 100 is the same as multiplying by 1/100. This turns 100/3 into 100/3 × 1/100 = 100/300.

Now simplify the resulting fraction. Both 100 and 300 have a greatest common factor of 100. Dividing both by 100 results in 1/3.

So, 33 1/3% as a fraction in lowest terms is 1/3. This method can be used for any percent, including those with decimals or fractions. The key steps are: convert the percent to a number over 100, change any mixed numbers to improper fractions, multiply, and simplify the result.