How would you convert the following into squared units
- 4,000 mm2 = m2
- 12.5 m2 =cm2
- 2km = m2
- 12 cm2 = mm2
- 4.5 m2 = mm2
- 56.8 cm2 = mm2
- 1 000 000 mm2 = cm2
- 5 billion cm2 = km2
- 6 x 1018 mm2 = km2
The last one appears to be the same as the one I asked (since you're in my class, I can understand that ), so you may want to look at this thread:
but i'll do the rest if it makes you comfortable. it won't help you on your midterm though if you don't try to get the method and try it yourself. which method did you like better, i did the first question two slightly different ways, which do you fancy?
now i'm going to walk you through question 2. don't just read what i did once and say you don't understand, re-read each sentence and each step, until you get it. if you are SURE that no matter how many times you read it you will not get it, then say so.
here goes. the question is:
12.5 m^2 = ? cm^2
since we want to go from m to cm, you look for the equation that i posted with 1 m = ? cm. when you find that, we're in business.
now i did post such an equation, it goes like this:
1 m = 10^2 cm
so, since 1 m is the same as 10^2 cm, it means that in the question, wherever i see 1m i can replace it with 10^2 cm, becuase they are the same thing, that's what being equal means.
so we have 12.5 m^2, since 1m = 10^2 cm
12.5 m^2 = 12.5 (10^2 cm)^2
see how i replaced the red text with the new red text, because they are the same thing. now all we have to do is simplify
now to raise something to a power to another power, we multiply the powers. that is, (x^m)^n = x^(m*n)
so (10^2)^2 = 10^(2*2) = 10^4
and (cm)^2 = cm^2
so we can just raise the 10^2 and cm to the second power as described above and keep them beside each other, which is another law of exponents.
that is, (x*y)^2 = x^2 * y^2
so, 12.5 (10^2 cm)^2 = 12.5 * (10^2)^2 cm^2
= 12.5 * 10^4 cm^2
= 1.25 x 10^1 * 10^4 cm^2 .........i changed 12.5 to scientific notation, i hope you know how to do that
now we have 10^1 * 10^4
a law of exponents says, that if we multiply the same base (in this case 10) we add the powers to get the new power, and raise the base to the new power.
so 10^1 * 10^4 = 10^(1 + 4) = 10^5
so, 1.25 x 10^1 * 10^4 cm^2 = 1.25 x 10^5 cm^2
so 12.5 m^2 = 1.25 x 10^5 cm^2
and we're done
For cm to m, take 100 x 100 (since it's squared) and divide since the answer in metres will be smaller than cm.
Sorry, I can't explain very good, but that's how I did it.
Jhevon, in the other thread when you showed me how to do the last one that was a little different, if this is the method you use (with all the stuff you did in this thread), it's completely different than what I remember from school for the basic ones that were asked in this thread. I missed the day with the one I asked, so I had no clue about that.
I guess there are several ways to do it.