Question

How would you correctly write these numbers in standard form? (a) `6,370,000` `m` (b) `0.000,000,000,000,000,000,000,000,000,000,911` `kg` (c) `300,000,000` `ms^-1`

Answer 1

`a) 6.37 xx 10^6` m
`b) 9.11 xx 10^-31` kg
`c) 3.0 xx 10^8` m/s

Explanation:

I assume by standard form you are referring to scientific notation? Both terms are used.

In standard form you need to have the number given in the form

`a xx 10^n` where

`a` is a number such that `1 <= a <10 " " and n " is an integer"`

This means that for `a` you have a number with one digit before the decimal point, multiplied by a power of `10`

Count how many places the point is moved:
If the number is greater than 1, the index of 10 is positive.
If the number is less than 1, the index of 10 is negative.

`a) 6color(red)(,370,000.) = 6.37xx 10^color(red)(6)`m

`b)0color(blue)(.000,000,000,000,000,000,000,000,000,000,9)11`
`= 9.11 xx 10^-color(blue)(31)` kg

`c) 3color(red)(00,000,000) = 3.0 xx 10^color(red)(8)` m/s