Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in 1.00 mile and (b) feet in 1.00 km.

This question is extracted from "University Physics with Modern Physics 15th Edition by Hugh Young (Author), Roger Freedman (Author)"

 

Algorithmic Solution:

 

Replace the unknowns with your values, and then copy and paste into WolframAlpha.com for the answer.

 

Starting with the definition 1 in. = 2.54 cm, find the number of (a) kilometers in mile and (b) feet in km.

 

Part a

 

( mi)((5280 ft)/(1 mi))((12 in)/(1 ft) )((2.54 cm)/(1 in))((1 m)/(100 cm))((1 km)/(1000 m))

 

Round to two decimal places and include units, km.

 

Part b

 

( km)((10^3 m)/(1 km))((10^2 cm)/(1 m))((1 in)/(2.54 cm))((1 ft)/(12 in))

 

Use scientific notation, round to two decimal places, and include units, ft.

 

Lesson:

 

Given: 1 inch (in.) = 2.54 centimeters (cm)

 

(a) Find the number of kilometers in 1.00 mile:

 

To find the number of kilometers in 1.00 mile, we need to perform a series of unit conversions:

 

1 mile = 5,280 feet (this is a well-known conversion)1 foot = 30.48 centimeters (since 1 foot is 12 inches, and 1 inch = 2.54 cm)Now, we can find the number of centimeters in 1.00 mile:

 

1 mile = 5,280 feet1 mile = 5,280 feet x 30.48 cm/foot (using the conversion factor from feet to cm)1 mile = 160,934.4 cm

 

Next, we'll convert centimeters to kilometers:

 

1 kilometer (km) = 100,000 centimeters (since 1 km = 1,000 meters, and 1 meter = 100 centimeters)

 

Now, let's perform the conversion:

 

1 mile = 160,934.4 cm1 mile = (160,934.4 cm) / (100,000 cm/km)1 mile = 1.609344 km

 

So, there are approximately 1.609344

 

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