Converting Units Very large and small

Some numbers are very large, like the distance between planets or how far light can travel in a second.  Some numbers are very small like the size of an atom, or the reaction time of a robot.  All of these measurements have units, and hence all also have units.

We already know how to convert units of length, area, capacity, mass and volume.  Now it's time to do these conversions using very large or very small numbers.

One of the easiest ways to do this, is using scientific notation, which we have already covered. 

One of the easiest ways to connect all these ideas together is through an example, let's try a question.  

Example

$0.0000621$0.0000621 light years is said to be the distance between Jupiter and the Earth.  

a) write this in scientific notation

b) using the value $9.4605284\times10^{12}$9.4605284×1012 kilometres in one light year, how many kilometres is it between Jupiter and Earth, to $3$3 significant figures.

c) how many metres is this?

Think: to answer this question we need to remember how to write using scientific notation, how to multiply using scientific notation, and how many metres there are in a kilometre ($1000$1000).

Do:

a) $0.0000621$0.0000621 is $6.21\times10^{-5}$6.21×10−5

b) $6.21\times10^{-5}\times9.4605284\times10^{12}=5.87\times10^8$6.21×10−5×9.4605284×1012=5.87×108 km

c) $5.87\times10^8$5.87×108 km = $5.87\times10^8\times10^3$5.87×108×103 metres (convert to metres)

                     = $5.87\times10^{11}$5.87×1011 m

Worked Examples

QUESTION 1

QUESTION 2

QUESTION 3