Which of the following values is the greatest?
A.
7/3
B.
5.2
C.
13/3
D.
5.15
The Correct answer and Explanation is:
The given options are:
A. 73\frac{7}{3}37
B. 5.2
C. 133\frac{13}{3}313
D. 5.15
To determine the greatest value, let’s convert the fractions to their decimal equivalents.
- Option A: 73\frac{7}{3}37
- 73=2.333…\frac{7}{3} = 2.333…37=2.333…
- Option B: 5.2
- This is already a decimal.
- Option C: 133\frac{13}{3}313
- 133=4.333…\frac{13}{3} = 4.333…313=4.333…
- Option D: 5.15
- This is already a decimal.
Now, comparing all the decimal values:
- Option A: 2.333…
- Option B: 5.2
- Option C: 4.333…
- Option D: 5.15
Among these, 5.2 is the greatest.
Detailed Explanation:
When comparing numerical values, it’s important to express them all in the same form to facilitate accurate comparison. Here, the fractions 73\frac{7}{3}37 and 133\frac{13}{3}313 were converted to their decimal equivalents so that they can be directly compared with the other decimal numbers.
- Option A, 73\frac{7}{3}37, is approximately 2.33. This value is smaller than all the other options.
- Option B, 5.2, is the largest value among all options, exceeding both 5.15 and 4.33.
- Option C, 133\frac{13}{3}313, is approximately 4.33. While it is larger than 2.33, it is still smaller than both 5.2 and 5.15.
- Option D, 5.15, is very close to 5.2, but it is slightly smaller.
To further emphasize, decimals like 5.15 and 5.2 may seem close in value, but small differences can have a significant impact on which is the greatest. For instance, the hundredth place difference between 5.15 and 5.2 indicates that 5.2 is indeed the larger number.
Understanding how to convert fractions to decimals and comparing the place value of decimal numbers are critical in accurately determining which number is the greatest. Therefore, the correct answer is Option B: 5.2.