Neil needs about 0.33 cup of sugar for his recipe.
The Correct Answer and Explanation is:
The correct answer is 1/3.
To determine which fraction is closest to 0.33, the most effective method is to convert each fraction into its decimal form. This allows for a direct and simple comparison of the values. The problem asks us to compare the decimal 0.33 with the fractions 1/3, 1/4, and 2/3.
Let’s begin by converting each fraction.
First, we convert 1/3 into a decimal by dividing the numerator, 1, by the denominator, 3. The result of 1 divided by 3 is 0.333…, a repeating decimal where the digit 3 continues infinitely.
Next, we convert 1/4 into a decimal. We divide 1 by 4, which gives us the exact value of 0.25. This is a terminating decimal.
Finally, we convert 2/3. Dividing 2 by 3 results in another repeating decimal, 0.666…, where the digit 6 repeats infinitely.
Now we have the three decimal values to compare with Neil’s required amount of 0.33 cup:
- 1/3 is approximately 0.333…
- 1/4 is 0.25
- 2/3 is approximately 0.666…
To find which is closest, we can calculate the difference between 0.33 and each of these decimal equivalents.
The difference between 0.33 and 1/3 (0.333…) is 0.333… minus 0.33, which equals 0.003…
The difference between 0.33 and 1/4 (0.25) is 0.33 minus 0.25, which equals 0.08.
The difference between 0.33 and 2/3 (0.666…) is 0.666… minus 0.33, which equals 0.336…
Comparing these differences (0.003…, 0.08, and 0.336…), it is clear that 0.003… is the smallest value. Therefore, the fraction 1/3 is mathematically closest to 0.33. In fact, 0.33 is often used as the rounded, two-digit approximation for the fraction 1/3
