The length of an object is seven
millimetres. Express this length in metres,
giving your answer in scientific form.
Let’s firstly recall some of our
conversions of metric units of length. There are 10 millimetres in one
centimetre. There are 100 centimetres in one
metre. Combining these facts tells us that
there are 1000 millimetres in one metre. This means that in order to convert
a value from millimetres to metres, we need to divide by 1000. Seven divided by 1000 is equal to
0.007. This means that seven millimetres
is the same as 0.007 metres.
This number is not in scientific
form as it would need to be written 𝑎 multiplied by 10 to the power of 𝑏, where
the absolute value of 𝑎 is less than 10 and greater than or equal to one and 𝑏 is
an integer. 0.007 written in scientific
notation is seven multiplied by 10 to the power of negative three. This is because the digits have
moved three places to get from 7 to 0.007.
We could’ve worked this out
directly from the calculation seven divided by 1000. 1000 is the same as 10 to the power
of three, or 10 cubed. Dividing by 10 to the power of
three is the same as multiplying by 10 to the power of negative three. Once again, we get the answer seven
multiplied by 10 to the power of negative three. This is the length of the object in