Video Transcript
What is 0.00007 written in
scientific notation?
A number is written in scientific
notation if it is written in the form 𝑎 multiplied by 10 to the power of 𝑏, where
the absolute value of 𝑎 must be less than 10 and greater than or equal to one and
𝑏 is a positive or negative integer. In this question, we want to write
0.00007 in scientific notation. Our first step is to find the first
nonzero digit in our number. In this question, there is only
one, the seven. We place a decimal point after this
digit. Have there been other digits after
this seven, we would’ve written these after the decimal point, for example,
7.124. In this case, there are no nonzero
digits after the seven, so we have 7.0, or just seven.
We will multiply this by 10 raised
to some power. Our value for 𝑏 will be negative
for small numbers. This is because raising 10 to a
negative power actually means we will be dividing. 10 to the power of negative four is
the same as one over 10 to the power of four. So, we’re actually dividing by 10
to the power of four, which will make the number smaller.
To work out the value of 𝑏, we
need to find the number of place values the numbers have moved or the number of
times the decimal point has moved to the left. To get from 7.0 to 0.00007, we move
our decimal point five places to the left. Therefore, our exponent is negative
five. As 7.0 is the same as seven,
0.00007 written in scientific notation is seven multiplied by 10 to the power of
negative five.
