tag:blogger.com,1999:blog-12342221.post1658955941546381163..comments2023-10-26T04:29:29.731-07:00Comments on The Marshfield Tattler: Physics Homework HelpMaritzahttp://www.blogger.com/profile/10729429896105375815noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-12342221.post-10598543233753603082009-01-28T20:44:00.000-08:002009-01-28T20:44:00.000-08:00Junior may well have gotten it right, I couldn't r...Junior may well have gotten it right, I couldn't remember by the time I wrote that post. But it shows you why I shouldn't be helping Junior with physics homework, since I can't remember this stuff!Maritzahttps://www.blogger.com/profile/10729429896105375815noreply@blogger.comtag:blogger.com,1999:blog-12342221.post-79163548804476197422009-01-28T14:29:00.000-08:002009-01-28T14:29:00.000-08:00a little note on the graph... the number of kids s...a little note on the graph... the number of kids should be the x-axis (along the bottom) becuase it's the independent variable. The laundry should be the y-axis (up the side) because it's the dependent variable.... the amount of laundry depends on the number of kids, not the reverse.<BR/><BR/>hope that helps in the future!Unknownhttps://www.blogger.com/profile/13465575468618126038noreply@blogger.comtag:blogger.com,1999:blog-12342221.post-40992783161192783222009-01-09T11:25:00.000-08:002009-01-09T11:25:00.000-08:00Thanks, Erin! I was trying to remember this and ex...Thanks, Erin! I was trying to remember this and explain it to Junior at the same time, and that was quite a struggle. Having your explanation as a handy reference will help the next time we work on this topic.Maritzahttps://www.blogger.com/profile/10729429896105375815noreply@blogger.comtag:blogger.com,1999:blog-12342221.post-405149548813768252009-01-09T07:03:00.000-08:002009-01-09T07:03:00.000-08:00Hey Marshfield -- the best way I know to make divi...Hey Marshfield -- the best way I know to make dividing and multiplying numbers in scientific notation stick is to realize why the shortcuts you mentioned work. You're right about the adding and subtracting exponents, but it's helpful to know why that works, just in case the problem gets mixed up, or to check your work.<BR/><BR/>Here's an example:<BR/>(2.1 x 10^3) x (4 x 10^4) = ?<BR/>If you were to write those out in standard form you'd get this problem:<BR/>(2100) x (40000) because the exponents on the power of ten move the decimal of the integer over to the right that number of spaces. ((Side note: Lots of people get confused and think of the exponent as adding on a certain number of zeros, but that's not really the case as you see in the example with 2.1)) <BR/><BR/>Multiplying out the problem in standard notation gives you 84000000. To convert this back to scientific notation you have to remember that the integer must have only one digit to the left of the decimal place so you use 8.4, (NOT 84) as your digit, giving you 8.4 x 10^? Now, ask yourself, what power of ten would move the decimal over the appropriate number of spaces? <BR/><BR/>10^0 = 8.4<BR/>10^1 = 84<BR/>10^2 = 840<BR/>10^3 = 8400<BR/>10^4 = 84000<BR/>10^5 = 840000<BR/>10^6 = 8400000<BR/>10^7 = 84000000 BINGO!<BR/><BR/>The solution is 8.4 x 10^7<BR/>Look back at the original problem:<BR/>(2.1 x 10^3) x (4 x 10^4) = ?<BR/><BR/>Instead of doing it the long way like we just did above, you can short cut it by multiplying the integers together then multiplying the powers of ten together:<BR/><BR/>(2.1 x 4) x (10^3 x 10^4) =<BR/>(8.4) x (10^7) =<BR/>8.4 x 10^7 just as we solved!<BR/><BR/>The same idea goes for division. The important thing for division, though, is to be sure to keep the order of the problem the consistent. For example: <BR/><BR/>(6 x 10^5) / (2 x 10^3) = <BR/><BR/>(6/2) x (10^5)/(10^3) = <BR/>3 x 10^2 because the exponents are subtracted (5 - 3 = 2)<BR/><BR/>I still recommend getting the hang of switching between standard and scientific notation because it helps to check your work. The above problem, then, becomes:<BR/><BR/>600000 / 2000 =<BR/>300 =<BR/>3 x 10^2<BR/><BR/>If the problem were reversed, it would be quite different: <BR/><BR/>(6 x 10^3) / (2 x 10^5) = <BR/>(6/2) x (10^3)/(10^5) = <BR/>3 x 10^(-2)<BR/>It's okay to have negative exponents. That just means that you're dealing with a fraction instead of a number greater than one. 3 x 10^(-2) = 0.03 or 3/100<BR/><BR/>Hope that helps some! This can be confusing sometimes but I'm sure it'll get easier with practice!Erinhttps://www.blogger.com/profile/16111776709485935864noreply@blogger.com