Convert 55mph to Millifurlongs per Microfortnight

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SUMMARY

The task is to convert a speed limit of 55 miles per hour into millifurlongs per microfortnight. The conversion process involves using the relationships that 1 mile equals 8 furlongs and 1 fortnight equals 336 hours. The correct conversion formula is 55 (mi/hr) * 8 (furlong/mi) * 1000 (millifurlong/furlong) * 336 (hours/fortnight) * 10^-6 (fortnight/microfortnight), which results in the desired units. This method effectively cancels out the unwanted units, leading to the correct answer.

PREREQUISITES
  • Understanding of unit conversion and dimensional analysis
  • Familiarity with speed measurement units (miles, furlongs, hours)
  • Basic knowledge of time measurement (fortnight, microfortnight)
  • Ability to manipulate fractions and perform multiplication with units
NEXT STEPS
  • Study dimensional analysis techniques for unit conversions
  • Learn about speed conversions between different measurement systems
  • Explore the concept of micro and milli prefixes in metric measurements
  • Practice additional unit conversion problems involving time and distance
USEFUL FOR

Students in physics or mathematics, educators teaching unit conversions, and anyone interested in understanding complex unit transformations in speed measurements.

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Homework Statement


The speed limit on a particular stretch of road is 55 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is 1/8 mile, and a fortnight is a period of 2 weeks.


Homework Equations





The Attempt at a Solution


so what I tried doing was taking

55 mph ( 8furlong/1mile ) ( 336hours/1fortnight ) = 147840

8 furlongs are in one mile and 336hours are in 1 fortnight. However the answer that I got isn't correct so I need to know what I'm doing wrong please.
 
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shortman12012 said:

Homework Statement


The speed limit on a particular stretch of road is 55 miles per hour. Express this speed limit in millifurlongs per microfortnight. A furlong is 1/8 mile, and a fortnight is a period of 2 weeks.


Homework Equations





The Attempt at a Solution


so what I tried doing was taking

55 mph ( 8furlong/1mile ) ( 336hours/1fortnight ) = 147840

8 furlongs are in one mile and 336hours are in 1 fortnight. However the answer that I got isn't correct so I need to know what I'm doing wrong please.

What you need to do is change mi/hr units to millifurlong/microfortnight units. It's helpful to write the units involved as fractions, because you want the units you don't want to cancel, so that you end up with the units you do want. For that reason I wrote mph as mi/hr.

Each of the expressions you have above in parentheses is a unit, hence is equal to 1. You can multiply by units all you want without changing the basic value of what you start with.

55 (mi/hr) * 8 (furlong/mi) * 1000 (millifurlong/furlong) * ...

The expression above converts miles per hour to millifurlongs per hour. Notice how the mi units cancel and the furlong units cancel. Tack on a few more units to get to millifurlongs/microfortnight.
 
if i take this and continue would the rest be
55 (mi/hr) * 8 (furlong/mi) * 1000 (millifurlong/furlong) * 336 (hours/fortnight) * 10^-6 (fortnight/microfortnight)?
 
ahh thank you, that's the correct answer, thank you for your help :)
 

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