what is 33 1/3% as a fraction in simplest form?
The Correct Answer and Explanation is:
Correct Answer:
33 1/3% as a fraction in simplest form is 1/3.
Explanation
To convert 33 1/3% into a fraction in its simplest form, we need to first understand what percent means. The word “percent” means “per hundred.” So, 33 1/3% literally means 33 1/3 out of 100.
Step 1:
Change the mixed number to an improper fraction.
33 1/3 can be written as:3313=100333 \frac{1}{3} = \frac{100}{3}3331=3100
This is because 33 times 3 equals 99, and 99 plus 1 equals 100. So 33 1/3% becomes 100/3%.
Step 2:
Convert percent to a fraction by dividing by 100.1003÷100=1003×1100=100300=13\frac{100}{3} \div 100 = \frac{100}{3} \times \frac{1}{100} = \frac{100}{300} = \frac{1}{3}3100÷100=3100×1001=300100=31
Now we simplify the fraction. 100 divided by 100 is 1, and 300 divided by 100 is 3, so we are left with 1/3.
Therefore, 33 1/3% as a fraction is 1/3.
Let us understand this conceptually. Percentages are simply another way to express parts of a whole. If you have 33 1/3% of something, it means you have just over one-third of that whole. Converting percentages to fractions helps when dealing with equations, ratios, or measurements where fractions are more convenient.
It is also useful to know that 33 1/3% is a repeating decimal in decimal form: 0.333… When you convert this decimal to a fraction, you again get 1/3. So whether you start with the percent, the decimal, or a part of a whole, all paths lead to the same final value: 1/3.
This conversion method can be applied to many percentages to help understand how parts relate to wholes in different contexts.
