Significant Figures and Scientific Notation
Date: 05/21/97 at 15:31:21 From: Tom Smith Subject: Physics 1) Round off 0.0049064 to four significant figures 2) How many significant figures does 1.00 have? I have trouble with significant figues. I don't know if I should count the numbers after the decimal point. I have to give a presentation in class about sig figs and I need to know if these problems are correct. Thank you.
Date: 06/05/97 at 19:59:23 From: Doctor Mandel Subject: Re: Physics Tom, To use significant figures, you need to first put the number into scientific notation. Scientific notation means writing a number as the first digit before the decimal and the rest of the number after the decimal (up to the zeros) all multiplied by a power of ten. For example, to write 12300 in scientific notation, you write the first digit before the decimal point and the rest of the digits after it, so you write 1.23. Then you figure out by what power of ten you have to multiply 1.23 by to get 12300. It's easier to think of this as, "How many decimal places do I have to move the decimal point to the left?" In this case, it would be 4 places to the left, so the full number would be 1.23 * 10^4. This number has three significant figures since, when written in scientific notation it has three digits. If the number is less than zero (.003 for example), you count how many places you move the decimal to the left to give you a negative number, so the power of ten is negative. Moving on to your problems, if you were to write 0.0049064 in scientific notation, you would write 4.9064 * 10^-3. This number has five significant figures since it is 4.9064, so to make it four significant figures you round it off until there are four digits, so you would make it 4.906 * 10^-3. If in a number there are zeros after the decimal point, they are there for a reason and should be counted as significant figures. Using another of your examples, 1.00 (* 10^0) has three significant figures because there are three digits present, not counting the ten to the whatever power. -Doctor Mandel, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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