Question

A scale says that its readings are accurate to within 1%, meaning that when an object is weighed using that scale, the reading will have an error of at most 1%. Gillian puts a math textbook on a scale, and the scale reads 1,999.8 grams. What is the difference between the maximum and minimum possible values for the textbook's actual weight?

A 19.998 grams
B 20.2 grams
C 39.996 grams
D 40 grams

Answer 1

The difference between the maximum and minimum possible values for the textbook's actual weight is 39.996 grams.

Step-by-step explanation:

To find the difference between the maximum and minimum possible values for the textbook's actual weight, we need to consider the 1% error range of the scale reading. The scale reads 1,999.8 grams, so the maximum possible weight would be 1% higher than this, and the minimum possible weight would be 1% lower.

To calculate the maximum value, we add 1% of 1,999.8 grams to the scale reading:
Maximum value = 1,999.8 + (1% of 1,999.8) = 1,999.8 + 19.998 = 2,019.798 grams

To calculate the minimum value, we subtract 1% of 1,999.8 grams from the scale reading:
Minimum value = 1,999.8 - (1% of 1,999.8) = 1,999.8 - 19.998 = 1,979.802 grams

Therefore, the difference between the maximum and minimum possible values for the textbook's actual weight is:
2,019.798 - 1,979.802 = 39.996 grams.