Dimensional Analysis (1.3.5)

Question 1

• A conversion factor is always a factor of one constructed from a known equality.

Answer 1

• A conversion factor is always a factor of one constructed from a known equality.

Question 2

• Multiple conversion factors are sometimes necessary when converting from one unit to another.

Answer 2

• Multiple conversion factors are sometimes necessary when converting from one unit to another.

Question 3

• Temperature conversions are simpler when the proper units are placed on the conversion factor.

Answer 3

• Temperature conversions are simpler when the proper units are placed on the conversion factor.

Question 4

A conversion factor is always a factor of one
constructed from a known equality. For example,
1 dollar = 106.823 yen, so 1 dollar / 106.823 yen =
106.823 yen / 1 dollar = 1.

Conversion factors are useful for converting one
quantity to another. For example, an amount in
dollars could be converted to yen by multiplying by
106.823 yen / 1 dollar. The dollars in the numerator
cancel with the dollars in the denominator, leaving
yen. This method of converting quantities by
multiplying by conversion factors to cancel units is
called dimensional analysis.

Answer 4

A conversion factor is always a factor of one
constructed from a known equality. For example,
1 dollar = 106.823 yen, so 1 dollar / 106.823 yen =
106.823 yen / 1 dollar = 1.

Conversion factors are useful for converting one
quantity to another. For example, an amount in
dollars could be converted to yen by multiplying by
106.823 yen / 1 dollar. The dollars in the numerator
cancel with the dollars in the denominator, leaving
yen. This method of converting quantities by
multiplying by conversion factors to cancel units is
called dimensional analysis.

Question 5

Multiple conversion factors are sometimes
necessary when converting from one unit to
another.

For example, miles per hour (mi/hr) can be
converted to meters per second (m/s) by using
multiple conversion factors to convert from miles to
feet, feet to inches, inches to centimeters,
centimeters to meters, hours to minutes, and
minutes to seconds. It is always good to check that
the units cancel properly. If not, a conversion factor
might have the numerator and denominator
reversed.

Answer 5

Multiple conversion factors are sometimes
necessary when converting from one unit to
another.

For example, miles per hour (mi/hr) can be
converted to meters per second (m/s) by using
multiple conversion factors to convert from miles to
feet, feet to inches, inches to centimeters,
centimeters to meters, hours to minutes, and
minutes to seconds. It is always good to check that
the units cancel properly. If not, a conversion factor
might have the numerator and denominator
reversed.

Question 6

Temperature conversions are simpler when the
proper units are place on the conversion factor.

For example, it is easier to make sure that the
proper conversion formula is used if units are placed
on the conversion factor from temperature in
degrees Celsius (T(˚C)) to temperature in degrees
Fahrenheit (T(˚F)). Temperature in degrees
Celsius (T(˚C)) can be converted to temperature on
the Kelvin scale (T(K)) by adding 273.15 K.

Units should always be carried along when making
conversions.

Answer 6

Temperature conversions are simpler when the
proper units are place on the conversion factor.

For example, it is easier to make sure that the
proper conversion formula is used if units are placed
on the conversion factor from temperature in
degrees Celsius (T(˚C)) to temperature in degrees
Fahrenheit (T(˚F)). Temperature in degrees
Celsius (T(˚C)) can be converted to temperature on
the Kelvin scale (T(K)) by adding 273.15 K.

Units should always be carried along when making
conversions.