MHB How to Convert Miles to Kilometers with a Conversion Chain

[karush]

Starting with the definition $1 in.=2.54 cm$ find km in 1 mi
$1 mi= \left(\dfrac{2.54cm}{1 in}\right)\left(\dfrac{63360 in}{1 mi}\right)\left(\dfrac{1 km}{100000 cm}\right)= km$
google says 1mi=1.60934km so something wrong with my conversion chain

here is a collection MHB replies I am sending to friends probably a typo here and there
using orangedox to count the downloads so far 5
https://dl.orangedox.com/6rStfn4eMFHuHvAKuX

 

[skeeter]

$\dfrac{5280 \, ft}{mile} \cdot \dfrac{12 \, in}{ft} \cdot \dfrac{2.54 \, cm}{in} \cdot \dfrac{1 \, m}{100 \, cm} \cdot \dfrac{1 \, km}{1000 \, m}$

 

[topsquark]

Starting with the definition $1 in.=2.54 cm$ find km in 1 mi
$1 mi= \left(\dfrac{2.54cm}{1 in}\right)\left(\dfrac{63360 in}{1 mi}\right)\left(\dfrac{1 km}{100000 cm}\right)= km$
google says 1mi=1.60934km so something wrong with my conversion chain

here is a collection MHB replies I am sending to friends probably a typo here and there
using orangedox to count the downloads so far 5
https://dl.orangedox.com/6rStfn4eMFHuHvAKuX

The units on the LHS are miles and the units on the right are km/mi. It's a sloppy way to set this up. I'd write it this way:
[math]1 ~ \text{mi} = \dfrac{1 ~ \text{mi}}{1} \cdot \dfrac{63360 ~ \text{in}}{1 ~ \text{mi}} \cdot \dfrac{2.54 ~ \text{cm}}{1 ~ \text{in}} \cdot \dfrac{1 ~ \text{km}}{100000 ~ \text{cm}}= 1.609344 ~ \text{km}[/math]

Also, many conversion factors are not exact. For example, it is true that 5280 ft = 1 mi exactly. But there didn't used to be exactly 2.54 cm in 1 in. (The inch was redefined after WWII.) So as long as your answer is at least close to the "correct answer" you are fine.

-Dan

 

[karush]

Starting with the definition $1 in.=2.54 cm$
find ft in km
$ \dfrac{1\ \cancel{in}}{2.54 \cancel{cm}}\cdot\dfrac{1\ ft}{12\ \cancel{in}}\cdot 10^5 \cancel{cm}$

google says $1 km = 3280.84 ft$

couldn't get it altho a simple problem

 

[topsquark]

Starting with the definition $1 in.=2.54 cm$
find ft in km
$ \dfrac{1\ \cancel{in}}{2.54 \cancel{cm}}\cdot\dfrac{1\ ft}{12\ \cancel{in}}\cdot 10^5 \cancel{cm}$

google says $1 km = 3280.84 ft$

couldn't get it altho a simple problem

Again you are being sloppy in how you are setting this up.
[math]1 ~ \text{km} = \dfrac{1 ~ \text{km}}{1} \cdot \dfrac{100000 ~ \text{cm}}{1 ~ \text{km}} \cdot \dfrac{1 ~ \text{in}}{2.54 ~ \text{cm}} \cdot \dfrac{1 ~ \text{ft}}{12 ~ \text{in}}= 3280.84 ~ \text{ft}[/math]

I don't know why you didn't get the Google answer.

-Dan

 

[karush]

Again you are being sloppy in how you are setting this up.
[math]1 ~ \text{km} = \dfrac{1 ~ \text{km}}{1} \cdot \dfrac{100000 ~ \text{cm}}{1 ~ \text{km}} \cdot \dfrac{1 ~ \text{in}}{2.54 ~ \text{cm}} \cdot \dfrac{1 ~ \text{ft}}{12 ~ \text{in}}= 3280.84 ~ \text{ft}[/math]

I don't know why you didn't get the Google answer.

-Dan

not sure why you have as the first term $\dfrac{1 km}{1}$ ?

this problem was a very popular online but so many sacred cows it just got more?
plus too much become a member with cc and we will help...
its better just to stay here
I was getting the numbers correct but the decimal was always way off

 

[topsquark]

not sure why you have as the first term $\dfrac{1 km}{1}$ ?

You want to know how many ft are in 1 km, so I started with 1 km. The 1 in the denominator is just a placeholder.

-Dan