Which of the following is the greatest value?
A.
74÷95
B.
7/8
C.
0.72
D.
74%
The Correct Answer and Explanation is:
To determine the greatest value among the given options, we should first convert all the options to the same format, preferably decimal form. This will make it easier to compare them directly.
Option A: ( \frac{74}{95} )
To convert this fraction into a decimal, we divide 74 by 95:
[ 74 \div 95 = 0.7789 \text{ (approximately)} ]
Option B: ( \frac{7}{8} )
Next, we convert the fraction ( \frac{7}{8} ) into a decimal by dividing 7 by 8:
[ 7 \div 8 = 0.875 ]
Option C: ( 0.72 )
This value is already in decimal form, so no further calculation is needed:
[ 0.72 ]
Option D: 74%
The percentage value can be converted to a decimal by dividing by 100:
[ 74\% = \frac{74}{100} = 0.74 ]
Comparison of Values
Now that all the options are in decimal form, we can compare them:
- Option A: ( 0.7789 )
- Option B: ( 0.875 )
- Option C: ( 0.72 )
- Option D: ( 0.74 )
Among these, the largest value is ( 0.875 ) (Option B).
Explanation
The process of comparison is straightforward once all numbers are in the same format. Fractions, percentages, and decimals can all be converted into decimal form, which allows for easy comparison.
- Fraction Conversion: Fractions represent a part of a whole. To compare fractions with decimals or percentages, converting them into decimals helps to see their exact value relative to 1.
- Percentage Conversion: Percentages represent a part out of 100. By converting percentages to decimals, you are seeing what portion of 1 the percentage represents.
- Direct Comparison: Once all numbers are in decimal form, you can directly compare the digits from left to right. The largest digit in the highest place value determines the greatest number.
In this case, ( \frac{7}{8} ) or 0.875 is the greatest value, as it is larger than 0.7789, 0.72, and 0.74. Understanding these conversions is crucial in solving problems that require comparing different forms of numerical expressions.