Question

The fundamental SI unit of length is meter.However we often deal with larger or smaller length or distances for which multiples or fractions of the fundamental unit are more useful. For each of the following situations suggest what fraction or multiple of the meter might be the most appropriate measurement.

Answer 1

The suggest units for each case are, respectively:

a) The distance between Chicago and Saint Louis - Kilometer.

b) The size of your bedroom - Meter.

c) The dimensions of this textbook - Centimeter.

d) The thickness of a hair - Micrometer.

Reminder - Question is incomplete, the complete statement is described below:

"The fundamental SI unit of length is meter. However, we often deal with larger or smaller length or distances for which multiplies or fractions of the fundamental units are more useful. For each of the following situations, suggest what fraction or multiple of the meter might be the most appropriate measurement:

a) The distance between Chicago and Saint Louis.

b) The size of your bedroom.

c) The dimensions of this textbook.

d) The thickness of a hair."

We can determine if a Unit is either a Multiple or a Fraction by using the following formula:

$\frac{Q_{u}}{Q_{r}} = 10^{n}$ (1)

Where:

$Q_{u}$ - Used unit, in meters.

$Q_{r}$ - Reference unit, in meters.

$n$ - Unit-to-unit factor, no unit.

A Measure has a Multiple of the Fundamental Unit if and only if $n> 0$, and it is a Fraction of the Fundamental Unit if and only if $n < 0$.

Now we proceed to analyze each case:

a) The distance between Chicago and Saint Louis - The Kilometer is the most common unit to measure Distance between Cities. A Kilometer has a Unit-to-unit factor of 3, representing a Multiple of the Meter.

b) The size of your bedroom - The Meter is the most common unit for Housing and Buildings. A Meter has a Unit-to-unit factor of 0, representing the Fundamental Unit itself.

c) The dimensions of this textbook - The Centimeter is the most common unit for dimensions of Books. A Centimeter has a Unit-to-unit factor of -2, representing a Fraction of the Meter.

d) The thickness of a hair - The Micrometer is the most common unit for the Thickness of a Hair. A Micrometer has a Unit-to-unit factor of -6, representing a Fraction of the Meter.

Then, the suggest units for each case are, respectively:

a) The distance between Chicago and Saint Louis - Kilometer.

b) The size of your bedroom - Meter.

c) The dimensions of this textbook - Centimeter.

d) The thickness of a hair - Micrometer.

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