Question

How do you write `0.005002` in scientific notation?

Answer 1

To write this term in scientific notation we need to move the decimal point 3 places to the right, therefore the exponent of the 10 will be negative:

`0.005002 = 5.002 xx 10^-3`

Answer 2

`5.002 xx 10^-3`

Explanation:

When working with scientific notation, a useful rule of thumb is:

If the decimal point moves to the LEFT:

`rarr` the power of `10` INCREASES by `1` for each place moved.

`" "4color(blue)(50,000,000.) xx 10^0 = 4.5 xx 10^color(blue)(8)`
`" ".larrlarrlarr." "`(the decimal point moved `8` places left)

If the decimal point moves to the RIGHT:

`rarr` the power of `10` DECREASES by `1` for each place moved.

`" "0color(red)(.000,784) xx 10^0 = 7.84 xx 10^color(red)(-4)`
`" ".rarr." "`(the decimal point moved `4` places right)

Sometimes in calculations, numbers are obtained which are not in scientific notation. These have to be adjusted so that there is only ONE digit before the point.

`17.3 xx 10^15 = 1.73 xx 10^16`

`156 xx 10^-9 =1.56 xx 10^-7`

`0.00423 xx 10^18 = 4.23 xx 10^15`

`0.000,008,91 xx 10^-5 = 8.91 xx 10^-11`