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

1 Answer

Answer:

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#