Start with the conversion

1ft = 30.48cm

if we divide both sides by 30.48cm we can see that

30.48cm/1ft = 1

similarly, for yards to feet

1yard = 3ft

and dividing by 1 yard we get

3ft/1yard = 1

Now, we have 100 yards and want to find out how many cm this is equivalent to. Lets convert the units. If we multiply by something by 1, we do not change the value

100yards = 100yards*1

but since we know

1 = 3ft/1yard

we can do

100yards = 100yards*(3ft/1yard)

100yards = 300ft

Now, to convert 300ft to cm, multiply by 1 in a similar way.

300ft = 300ft*1

and we know

1 = 30.48cm/1ft

so

300ft = 300ft*1 = 300ft*(30.48cm/1ft)

300ft = 9144cm

9144cm in 300ft, and therefore 9144cm in 100 yards.

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