Significant figures?

Question

1) 101.69 * 23.847

Also, how do I know what to put my answers in scientific notation? Let's just say that I get an answer that is something like 22.66 and the answer was supposed to have 4 significant figures. Do I need to put the answer in scientific notation or no?

Thanks for your help!

* sorry, I meant "when" not "what" in my question.

Answer 1

101.69 * 23.847 = 2425.0014, so the calculator says
However, the first figure only has two places after the decimal point, so the answer is accurate to only two decimal places. This makes the answer 2425.00 and the last figure remains "0" because the next figure is less than 5 (it's a "1"). If it were "5" then check the next figure following it. For example, if 1.0056 were rounded to two places, 1.01 would be the answer. If all one had to work with were 1.005, it seems to be a matter of choice. Some teachers round up to 1.01 and some will leave the answer 1.00.

Reguarding scientific notation, most people working technical jobs use "fortran" syntax. Fortran is a computer language and represents expoentials with the letter "E". For example, "two point three times ten to the third power" would be "2.3E3" in Fortran syntax. The answer above would be 1.0169E2 times 2.3847E1 and 2.4250E3 would be the answer. In scientific notation, all the numbers had four significant figures, and the answer did too. Since the numbers were represented in scientific notation, the answer was, too. Note however, that the scientific notation answer has dropped one of the trailing zeros.

Answer 2

1) 2425.0

The reason to put numbers in scientific notation is if you have very small or large numbers, and it's easier to calculate with "numbers" separate from exponents. (Another reason is because the teacher tells you to.) You may have one number like 6.02x10^23, and that sets the stage for what's easiest or most obvious next.