Question

The value of = 40.01 is much greater than 1.Penny then Without computing, decide whether the value of each expression is much smaller than

1, close to 1, or much greater than 1.
a. 100:1000
b. 50 - 501
c. 4.7-5.2

Answer 1

The expressions result in the following comparisons to 1: a) 100:1000 is much smaller than 1, b) 50 - 501 is much greater than 1 in magnitude, and c) 4.7-5.2 is close to 1 in absolute value.

Step-by-step explanation:

The student's question requires us to determine whether the value of each mathematical expression is much smaller than 1, close to 1, or much greater than 1. Let's examine each expression:

• a. 100:1000 - When considering the ratio of 100 to 1000, we simplify this to 1:10. Thus, the value is 0.1, which is much smaller than 1.
• b. 50 - 501 - This expression results in a negative number (-451), which does not apply to being smaller or greater in the context of this question. However, the magnitude of the result is much greater than 1 in absolute terms.
• c. 4.7-5.2 - Subtracting 5.2 from 4.7 gives us -0.5. Again, this is a negative result, but considering the absolute value, 0.5 is close to 1.

It is important to remember that when dealing with ratios, a numerator smaller than the denominator gives a value smaller than 1. For subtraction, if the number being subtracted is larger than the number from which it is being subtracted, the result will be negative.