Comparing Rational Numbers: TEAS Practice Question with Answer & Explanation

Understanding the Comparison of Real Numbers

To compare a mix of decimals and fractions accurately on the TEAS, the most reliable strategy is to convert all values into the same format. Usually, converting everything to decimals is the fastest and least error-prone method.

Step-by-Step Conversion and Comparison

Let’s evaluate each choice:

1. A: 2.65
   This value is already in decimal form.

2. B: 13/5
   To convert a fraction to a decimal, divide the numerator by the denominator.
   $13 \div 5 = 2.60$.

3. C: 2.585
   This value is already in decimal form. When comparing, it helps to add "placeholder zeros" so all decimals have the same number of digits. Thus, we can view this as $2.585$.

4. D: 8/3
   Divide 8 by 3.
   $8 \div 3 = 2.666...$ (or $2.\overline{6}$).

The Final Comparison

Now, let's align our values to the same number of decimal places for an easy "apples-to-apples" comparison:

• Choice A: 2.650
• Choice B: 2.600
• Choice C: 2.585
• Choice D: 2.666...

When we compare these values, 2.666... is clearly larger than 2.650, 2.600, and 2.585. Therefore, 8/3 is the greatest value.

Why the Other Answers are Incorrect

• Choice A (2.65): While larger than 2.60 and 2.585, it is smaller than 2.666 (8/3).
• Choice B (13/5): This equals exactly 2.6. In a list of numbers like this, it is easy to mistake this for being "large" if you don't perform the division carefully, but it is actually smaller than A and D.
• Choice C (2.585): This is the smallest value in the set. Don't be fooled by the fact that it has more digits after the decimal point; the value is determined by the tenths and hundredths place.

TEAS Math Study Tip

When comparing decimals, always "pad" the numbers with trailing zeros so they are all the same length (e.g., change 2.6 to 2.600). This prevents the common mistake of thinking a "longer" decimal like 2.585 is larger than a "shorter" decimal like 2.6.