Alessandra Posted October 27, 2011 Share Posted October 27, 2011 These are some scientific notation problems. The ^ indicates a superscript, as in 10 to the 3rd. a) -4.56 x 10^-3 b) 4.56 x 10^2 c) -4.56 x 10^2 d) 4.56 x 10^-2 The answers to b & d are straightforward, but what about a & c? a) -4,560 ?????????????????????????? b) 456 c) -0.0456 ?????????????????????????? d) 0.0456 Can someone explain if this is correct and, if so, why? Or if it is not correct, how do you solve these problems? (Cross posted on curriculum board) Quote Link to comment Share on other sites More sharing options...
SJ. Posted October 27, 2011 Share Posted October 27, 2011 (edited) These are some scientific notation problems. The ^ indicates a superscript, as in 10 to the 3rd. a) -4.56 x 10^-3 = -0.00456 b) 4.56 x 10^2 = 456 c) -4.56 x 10^2 = -456 d) 4.56 x 10^-2 = 0.0456 The answers to b & d are straightforward, but what about a & c? a) -4,560 ?????????????????????????? b) 456 c) -0.0456 ?????????????????????????? d) 0.0456 Can someone explain if this is correct and, if so, why? Or if it is not correct, how do you solve these problems? (Cross posted on curriculum board) My answers are in blue. I am definitely not good at math but we went over a lot of exponents in a biology class I took a year ago. The way I remember it is to move the decimal point to the left for negative exponents and to the right for positive. For some reason the instructor did not want us to think of it that way, but I don't remember why. Maybe someone else can give a better answer. ETA: I typed the problems in google (which acts like a calculator!) and the answers in blue are the same. SJ Edited October 27, 2011 by SJ. Quote Link to comment Share on other sites More sharing options...
Jacquelyn in NC Posted October 27, 2011 Share Posted October 27, 2011 I agree with the answers given above in blue. It looks like there's an error in your book's answers. The way I remember it is that a positive exponent means you have a large number while a negative exponent gives you a small number (under 1). Quote Link to comment Share on other sites More sharing options...
joannqn Posted October 27, 2011 Share Posted October 27, 2011 A negative exponent means you need to take the reciprocal. Problem A would be: -4.56 x 1/10^3 = -4.56 x 1/1000 = -4.56/1000 = -.00456 Problem B is just a negative number multiplied by 10^2: -4.56 x 10^2 = -4.56 x 100 = -456 Quote Link to comment Share on other sites More sharing options...
Alessandra Posted October 27, 2011 Author Share Posted October 27, 2011 (edited) My answers are in blue. I am definitely not good at math but we went over a lot of exponents in a biology class I took a year ago. The way I remember it is to move the decimal point to the left for negative exponents and to the right for positive. For some reason the instructor did not want us to think of it that way, but I don't remember why. Maybe someone else can give a better answer. ETA: I typed the problems in google (which acts like a calculator!) and the answers in blue are the same. SJ Oh, I hadn't thought of googling it I agree with the answers given above in blue. It looks like there's an error in your book's answers. The way I remember it is that a positive exponent means you have a large number while a negative exponent gives you a small number (under 1). The book didn't have answers, or an explanation for when the base is negative. A negative exponent means you need to take the reciprocal. Problem A would be: -4.56 x 1/10^3 = -4.56 x 1/1000 = -4.56/1000 = -.00456 Problem B is just a negative number multiplied by 10^2: -4.56 x 10^2 = -4.56 x 100 = -456 Thinking of the reciprocal makes sense. But -- perhaps it is late and I'm simply going insane, but isn't -4.56 larger than -456? I normally think that, in scientific notation, multiplying by 10^positive number makes the original number bigger, not smaller. That's what I am having trouble getting my head around. I guess I never really though about the implications of multiplying a negative and a positive number in this situation. I was probably making it too complicated -- I should have just moved the decimal points to the right and left, as with positive numbers. Yikes! Thank you all! ETA Found the converter on google. And I see I originally had the correct answers -- I just didn't believe them. Edited October 27, 2011 by Alessandra Quote Link to comment Share on other sites More sharing options...
kiana Posted October 27, 2011 Share Posted October 27, 2011 a) If you run into problems like this again and simply want to double-check your work, consider wolfram alpha. b) Think of larger versus smaller in *absolute* value (distance away from 0). Multiplying -4.56 by 10^2 will move it further away from 0 in the negative direction. Multiplying 4.56 by 10^2 will move it further away from 0 in the positive direction. Quote Link to comment Share on other sites More sharing options...
Alessandra Posted October 27, 2011 Author Share Posted October 27, 2011 a) If you run into problems like this again and simply want to double-check your work, consider wolfram alpha. b) Think of larger versus smaller in *absolute* value (distance away from 0). Multiplying -4.56 by 10^2 will move it further away from 0 in the negative direction. Multiplying 4.56 by 10^2 will move it further away from 0 in the positive direction. Never heard of Wolfram Alpha -- I just opened it in another window & will check it out. Yes, I forgot about absolute value. Now I am picturing this as a distance under water and I get it. My brain was obviously on vacation! Thank you for taking the time to post. And thank you for reminding me of absolute value -- now I can go to sleep without this bugging me, lol. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.