Convert to scientific notation.

Question

Convert to scientific notation.

a). -0.0001

b). 52x10⁴

Answer 1

For the term, -0.0001, I will break it down to it's most basic premise. We get two bits of information: it's negative, and it's in decimal form. As such, we can express our scientific notation the form: x * 10^-y, in which case we're essentially exponentiating base 10 as a denominator.

Counting our decimal places from right to left, stopping at the 10ths place, we take our mantissa (the number following the decimal point): [-1] and multiply it by [10^-4], so: -1 x 10^-4.

The expression, 52 x 10⁴ technically results in 520,000. By rewriting it to 5.2 x 10⁴, we complete the scientific notation and come up with the intended 52,000.

Answer 2

It's all about the format -- in this case #.# x 10^#.

For -0.0001, count how many times you move the decimal point from where it is

to right after the 1. 4, right? So it's #.# x 10^-4 (minus needed to get you back

to where you started from). The #.# is -1.0 (the starting minus stays put and the

zero is a place holder to show there's nothing after the 1).

For 52 x 10^4, the rules call for 52 to be 5.2 so the 10^4 needs to go up one to

10^5 so you get the same final product as 52 x 10^4. Are we having fun yet?

Answer 3

a.) -10^-4

b.) 520000