Find the range of the following set of numbers 0.4, −0.4, 0.3, 0.47, −0.53, 0.2 and −0.2

Analysis

To find the range of a set of numbers, you must identify the difference between the highest value (maximum) and the lowest value (minimum) in the data set.

Formula:

Step-by-Step Solution

Step 1: List the numbers and identify the maximum and minimum values. The given set is: $0.4, -0.4, 0.3, 0.47, -0.53, 0.2, -0.2$

• Positive numbers: $0.4, 0.3, 0.47, 0.2$
• Negative numbers: $-0.4, -0.53, -0.2$

Comparing the positive numbers, the largest is $0.47$. Comparing the negative numbers, the smallest (the one furthest to the left on the number line) is $-0.53$.

Step 2: Apply the range formula.

Step 3: Perform the calculation. When you subtract a negative number, it becomes addition:

Conclusion

The range of the set is $1.0$. Comparing this to your options: A. 1.03 B. 0.07 C. 0.03 D. 1.0

The correct option is D.

Exam Tip

Always be careful with signs when dealing with negative numbers! A common mistake is to simply subtract the absolute values (e.g., $0.47 - 0.53$). Remember that subtracting a negative is the same as adding the positive equivalent. Always visualize the number line if you are unsure which number is "smaller."