Question

1. how do you see it? match each description with its graph. which types of real numbers shown in figure p.1 on page 2 may be included in a range of prices? a range of lengths? explain. (i) 1.87 1.88 1.89 1.90 1.91 1.92 1.93 (ii) 1.87 1.88 1.89 1.90 1.91 1.92 1.93 (a) the price of an item is within $0.03 of $1.90. (b) the distance between the prongs of an electric plug may not differ from 1.9 centimeters by more than 0.03 centimeter.

Explanation:

Step1: Analyze the price - range description

The price of an item is within $0.03$ of $1.90$. So the range is $1.90 - 0.03\leq x\leq1.90 + 0.03$, which is $1.87\leq x\leq1.93$. This is a continuous range of values, which matches the interval notation in graph (i).

Step2: Analyze the length - range description

The distance between the prongs of an electric plug may not differ from 1.9 centimeters by more than 0.03 centimeter. So the range is $1.9 - 0.03\leq y\leq1.9+ 0.03$, which is $1.87\leq y\leq1.93$. This is also a continuous range of values and matches the interval notation in graph (i). Real - numbers in the range of prices and lengths are likely to be rational numbers (since prices are often given as decimal values with a limited number of decimal places and lengths are usually measured to a certain level of precision), but all real numbers in the interval $[1.87,1.93]$ are possible.

Answer:

(a) matches (i)
(b) matches (i)
Types of real numbers likely include rational numbers (due to measurement and pricing precision), but the interval $[1.87,1.93]$ contains all real numbers in that range.