Which of the following lists shows the correct ascending order (from smallest to largest) of the numbers 1/3, 4/15 and 0.33?

Introduction / Context:
This question asks you to compare fractions and a decimal and then arrange them in ascending order. It tests your ability to convert between forms or to compare numbers using a common baseline, such as decimal approximations.

Given Data / Assumptions:
The numbers to compare are 1/3, 4/15 and 0.33.We must order them from smallest to largest.Standard decimal value comparisons apply.

Concept / Approach:
A straightforward method is to convert all numbers to decimals or to convert them to a common denominator. Here, converting fractions to decimal form is quick. We approximate their decimal values and compare them. It is important to recall that 1/3 is approximately 0.3333 repeating, and 0.33 is close but slightly less.

Step-by-Step Solution:
Step 1: Convert 1/3 to a decimal. 1 divided by 3 is approximately 0.3333 repeating.Step 2: Convert 4/15 to a decimal. Compute 4 divided by 15, which is approximately 0.2666 repeating.Step 3: The decimal 0.33 is already given and equals 0.33 exactly.Step 4: Compare the decimal values: 0.2666..., 0.33 and 0.3333....Step 5: Clearly, 0.2666... (which corresponds to 4/15) is the smallest.Step 6: Next, 0.33 is slightly less than 0.3333..., so 0.33 is in the middle.Step 7: The largest value is 0.3333..., corresponding to 1/3.Step 8: Therefore, the correct ascending order is 4/15, 0.33, 1/3.

Verification / Alternative check:
To verify using fractions, express each number with a common denominator, for example 300. Then 1/3 equals 100/300, 4/15 equals 80/300 and 0.33 is approximately 99/300. The order 80/300 < 99/300 < 100/300 confirms that 4/15 is smallest, 0.33 is next and 1/3 is largest.

Why Other Options Are Wrong:
Any option that places 1/3 before 4/15 is incorrect because 1/3 is larger than 4/15. Options that put 0.33 after 1/3 mistakenly treat them as equal or reversed, ignoring that 0.33 is slightly less than 0.3333 repeating. Only the ordering 4/15, 0.33, 1/3 matches the correct comparison.

Common Pitfalls:
Some learners assume 0.33 equals exactly 1/3, which is not true, and therefore may place them in the wrong order. Others might compare the fractions without converting and mis-handle the denominators. Using decimal approximations or a common denominator carefully avoids such errors.

Final Answer:
The correct ascending order is 4/15, 0.33, 1/3.