Standard Form Question?

Question

I was doing quite well with my standard form questions but this one has thrown me

Write in standard form

980 x 10-3 ( this -3 is a power of ten sitting at top of the 10 cant do that on my computer )

I know the answer to be 9.8 x 10-1 ( again small -1 above the ten ) but i just dont get it how has the -3 changed to a -1 ????
I really need this written out in steps if possible thank you for your help.

Answer 1

To change the number in to standard form the 'number' part...i.e. 980 needs to be a number between 1 and 10



980 x 10⁻³ tells us the decimal point needs moving 3 places to the left



Well, changing 980.000000 to 9.8 moves the decimal point 2 places to the left...so, we only need to move the point 1 place to the left



i.e. 980 x 10⁻³ = 9.8 x 10⁻¹



:)>

Answer 2

10^(-3) is equal to 1/10^3 which is equal to 1/1000. ('^' means 'to the power of').

Multiplying 1/1000 is the same as dividing by 1000.

So 980/1000 is as you said 0.98 = 9.8 x 10^(-1)



Another way to think about is that to get 980 to standard form, the 1st digit needs to be just before the decimal point. To get 980 to 9.8, you divide by 100. Because you have divided one number by 100, you need to add 2 (or what ever the number of zeros) to the original number sitting on top of the ten so -3+2=-1.

Answer 3

standard form of scientific notation?

980 x 10-3,this is not in standard form

9.8 x 10^2 x 10^-3

9.8 x 10^-1

Answer 4

The decimal point has moved to the left by two points, each time subtracting a power from the number above the ten. (which BTW, is computer numerated as 9.8x10^-1) the (^) is the key computer asci character to indicate a number to the power of ten.

Answer 5

standard form of

980x10^-3 = 9.80x100x10^-3

=9.8x10^2x10^-3

=9.8x10^(2-3) [ a^m.a^n=a^(m+n) ]

=9.8x10^-1