Question

By using estimation techniques, arrange these items in order from shortest to longest: a \(57-\mathrm{cm}\) length of string, a 14 -in. long shoe, and a \(1.1-\mathrm{m}\) length of pipe.

Short answer

First, convert all measurements to centimeters: the string is already 57 cm, the shoe is \(14 \times 2.54 = 35.56\) cm, and the pipe is \(1.1 \times 100 = 110\) cm. Then, arrange them from shortest to longest: 14-inch shoe (35.56 cm), 57-cm string (57 cm), and 1.1-meter pipe (110 cm).

Step-by-step solution

Decide on a common unit of measurement

In order to arrange the objects in order of their lengths, we must first convert all units to a common unit of measurement. Here, we can convert all the measurements to centimeters since it is the easiest conversion for all given measurements.

Convert all lengths to the chosen unit of measurement

We will convert the length of each item to centimeters: 1. The length of a string is already given in centimeters, which is 57 cm. 2. To convert the shoe length from inches to centimeters, we will use the conversion 1 inch = 2.54 cm. Length of the shoe = 14 inches * 2.54 cm/inch = 35.56 cm 3. To convert the pipe length from meters to centimeters, we will use the conversion 1 meter = 100 cm. Length of the pipe = 1.1 meters * 100 cm/meter = 110 cm

Arrange the items in order of their lengths

After converting all lengths to centimeters, we have: 1. Length of string = 57 cm 2. Length of shoe = 35.56 cm 3. Length of pipe = 110 cm Now we can easily arrange them from shortest to longest: 1. 14-inch long shoe (35.56 cm) 2. 57-cm length of string (57 cm) 3. 1.1-meter length of pipe (110 cm)