write 0.000012 in scientific notation

Question

a. 1.2x10power of -5

b. 1.2x10power of 5

c. 12x10 power of 6

d. 12x10power of -6

Answer 1

So we wanna know what 0.000012 is in scientific notation.

With scientific notation, you want to end up with something that looks like number times ten raised to the power of x, which would look like:
numberx10^x.

The number in the front must always be more than 1, but less than 10. This means the number can be anything from 1.0 to 9.9.

So for the problem you have here we have 0.000012. This means the smallest number in the front could be 1.2 Not 12 and not .12 The number in the front must always be more than 1, but less than 10.

So now we have the first part of the scientific notation: 1.2x10. To know what power to raise the 10 to, count how many zeros there are to the right after the decimal. With our 0.000012, there are 4 zeros, which means 4 spaces to the right, so the 10 would be raised to -4

BUT if we raised that 10 to the power of -4, our notation would look like 0.12x10^-4 and remember, that first number cant be lower than 1.

So, we look back at our original number 0.000012, and we know that 10^-4 is wrong, so count the number of zeros, and then the first digit past the last zero: 0.000012 now that's 5 spaces which means we raise the 10 to a power of -5.

Notice now how when we write it out in the scientific notation, that last 5th digit is where we would put the decimal: 1.2x10^-5 

I hope that written out explanation helps a little better

Christina

Edited to fix my error ^_^;

Answer 2

The answer is 1.2x10^-5

10⁵ would be 10*10*10*10*10 = 100000

10^-5 would be a fraction: 1 / (10*10*10*10*10) = 1 / 100000 = 0.00001
1.2 x 0.00001 = 0.000012
1.2 x 10^-5= 0.000012

Just count the number of places you have to move the decimal point in 0.000012 to make it 1.2.  If you move it to the right, that number will be a negative exponent.  If you move it to the left, it would be a positive exponent.