Convert the following number to decimal notation, keeping the same number of significant figures: 3.20x10^-4

Answer 1

First let's convert to a decimal --

3.20 x10^-4

Know that a negative exponent moves the decimal TO THE LEFT. Remember - it makes the number SMALLER --

In this case I need to the move the decimal point 4 places to the LEFT, and this number becomes .000320

Significant figures has to do with how accurately you know the number - that is to what resolution you know the number. Zeros at the end of a number AFTER a decimal point are significant - because they are not merely placeholders (to make other numbers line up in the right place value) - it is telling you that the value in that place is determined to be 0, (not 1,2,3 or 4, or completely unknown) to the best of one's ability to determine (round) number in that place value.

In the given number 3.20 x10^-4 has 3 significant figures.

In the decimal form, .000320 also has 3 significant figures.

The zeros between the decimal and the 3 are NOT significant - they are merely there to make sure the 3, and the rest of the number, winds up in the right place to give a value equal to the original value.

So .000320 equals the given number and has the same number of significant digits as the given number,

I can equally have written 0.000320.