Question

How do you convert `2.3 x10^-2` into expanded notation?

Answer 1

The correct answer should be:
`6*10^-2x`

Explanation:

By definition, expanded notation produces an expression which represents each place holder's value.

NB: Standard notation is always represented by the sums of all the values multiplied by `10^"to the power of any number"` which should equal the original expression.

for e.g.
428 = `4*10^2 +2*10^1+8*10^0`

However, this question takes this idea one step further and introduces decimal places.

By using the above example, if we were given 428.39,
this would be expressed as:

428.39 = `4*10^2 + 2*10^1 + 8*10^0 + 3*10^-1 + 9*10^-2`

Beautiful isn't it.

As one can see, the degree (the exponents) of the `x's` are consecutively decreasing by one as one moves down every unit placeholder.

With this in mind, by looking at your question, `2.3x10^-2`, we can apply the same trend.

Step one: (turn the expression into decimal format)

`2.3x10^-2`,

`=6/(10^2)x`

`=6/(100)x`

`=0.06x`

Step Two: (convert to Standard notation)

Since this expression only has one numerical value of 6 which is occupying the hundredth's position, we multiply 6 by `10^-2` as this is equal to 0.06.

Now with regards to the algebraic terms, such as `x` in this case, since these variables are unknown and can have any value, they are left unaltered.

For term clarity,
"Numerical Form" of 42 has a "Standard Form" of 40 + 2 which can be expressed in the "Standard Notation" of `4*10 + 2*10^0`