How do you convert 1.47 km/h to mm/s?

#color(magenta)("You do it in stages")#

#color(blue)("Consider distance")#

1 Km = 1000 metres so #1.47Km = 1.47 xx 10^3 "metres"#

1 metre = 1000 mm so

#" "1.47 xx 10^3 " metres = " 1.47 xx 10^3 xx10^3" mm" #

Thus the total distance is #1.47xx10^6# in mm
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#color(blue)("Consider the time:")#

1 hour = 60 minutes

But 1 minute = 60 seconds

So 1 hour = #60 xx 60 = 3600# seconds

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#color(blue)("Putting it all together")#

# 1.47/(color(magenta)(1)) (Km)/h -= (1.47xx10^6)/(3600)" " (mm)/s#

Notice I put a #color(magenta)(" 1 ")#as a denominator for Km/#color(magenta)("h")#. This is in keeping with the single hour in Km/h

So all we need to do now is to change the 3600 seconds into 1 second but in doing so still retain the ratio of millimetres to seconds.

To maintain proportionality what you do to the bottom you also do to the top (Only works for multiply or divide).

Divide by 3600

#" "color(brown)((1.47-:3600xx10^6)/(3600-:3600))#

But 3600 is the same as #0.3600xx10^4#

So for the numerator we have #(1.47)/0.36xx10^6/10^4#

#= 4.083bar3xx10^2#

For the denominator #3600-:3600=1#

#color(brown)((1.47-:3600xx10^6)/(3600-:3600) = (4.083bar3xx10^2)/1" " (mm)/s)#

This would normally be written as

#" "color(blue)(4.083bar3xx10^2 " mm/s")#
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The bar 3 as #bar3# means that it goes on for ever with 3

in that we have 4.08333333333......