Question

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

Short answer

The shortest to longest arrangement is: shoe (35.56 cm), string (57 cm), and pipe (110 cm).

Step-by-step solution

Conversion of units

First, we convert the lengths into the same unit (centimeters). To do so, we can use the following conversion factors: 1 meter = 100 centimeters 1 inch = 2.54 centimeters

Convert the shoe length

The shoe length is given in inches. We will convert it to centimeters using the conversion factor mentioned above: Length of shoe = 14 inches × 2.54 cm/inch = 35.56 cm

Convert the pipe length

Now, we will convert the given length of pipe, which is in meters, to centimeters: Length of pipe = 1.1 m × 100 cm/m = 110 cm

Arrange the items from shortest to longest

We have the converted measurements for the three items: - Length of string: 57 cm - Length of shoe: 35.56 cm - Length of pipe: 110 cm Now, we can arrange these items in ascending order of their lengths: 35.56 cm (shoe) < 57 cm (string) < 110 cm (pipe) So, the arrangement is: shoe, string, and pipe.

Key concepts

Measurement

Measurement is a fundamental concept in both everyday life and in the sciences. It involves determining the size, length, or amount of something, typically compared to a standard unit. Often, measurements are obtained using tools like rulers, measuring tapes, or scales, which can provide a numerical value that represents a physical quantity such as length, weight, or volume.

When we measure, it's crucial to use the correct units to express the measurement, especially when comparing different items. The exercise provided illustrates a practical situation: arranging objects by length. To do this accurately, we first need to make sure all items are measured in the same unit. This is where unit conversion plays a role. By converting inches to centimeters and meters to centimeters, we can clearly see which item is the shortest and which is the longest. Without such conversions, comparing different measurements would be like comparing apples to oranges—confusing and unproductive.

Understanding how to measure and convert units is a critical skill that aids in making precise and useful comparisons in a wide range of activities, from crafting and construction to science experiments and engineering.

Estimation Techniques

Estimation techniques are methods used to find an approximate value when exact data is unavailable, impractical, or unnecessary. This includes rounding off numbers, making educated guesses based on experience, or using certain rules of thumb. The ability to estimate effectively is a valuable skill, helping to save time and simplify complex problems into more manageable ones.

In the original exercise, estimation did not play a primary role as we were aiming for precise conversions of the measurements. However, if precise tools or details are not available, estimation techniques can be applied. A key component of estimation in measurement is understanding the relative sizes of different units. For instance, knowing that a meter is larger than a centimeter helps you estimate that a 1.1-meter pipe is likely longer than a piece of string measured in centimeters. In situations where exact measurements aren't necessary, proficient estimation can make tasks like planning a room layout or purchasing materials more efficient.

Metric System

The metric system is an international decimal system of measurement that is based on the meter, liter, and gram as units of length, capacity, and mass, respectively. It is simple, universal, and allows for easy conversion between units, using powers of ten. For example, 1 meter equals 100 centimeters and 1 kilogram equals 1000 grams. This system is widely used around the world and is the standard system of measurement in science.

The exercise showcases the utility of the metric system in practical applications. By working within the metric system, conversion between units is straightforward and systematic. Since meters and centimeters are both metric units of length, converting from one to the other merely requires multiplication or division by a power of ten. The accessibility and coherence of the metric system simplify calculations and measurements, which is why understanding how to work within this system is essential for students in a range of disciplines.