October 6, 2021 at 2 PM Eastern/11 AM Pacific
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LEARN MORECan someone show me the quickest step to turn
(0.275/0.225) into (11/9)
Can someone show me the quickest step to turn
(0.275/0.225) into (11/9)
multiply top and bottom by 4
I don't mean to hijack the thread, but what about 10^-3.7?
TBR says "10^-3.7 = (10^0.3)*10^-4"
What in the ****? What is the method behind that? It's nice how they don't even mention this technique but they thought it was appropriate to have a page-long table that painstakingly confirms log(ab)=log(a)+log(b) and log(a/b)=log(a)-log(b).
I don't mean to hijack the thread, but what about 10^-3.7?
TBR says "10^-3.7 = (10^0.3)*10^-4"
What in the ****? What is the method behind that? It's nice how they don't even mention this technique but they thought it was appropriate to have a page-long table that painstakingly confirms log(ab)=log(a)+log(b) and log(a/b)=log(a)-log(b).
That's the same as 10^(a+b)=10^a*10^b. It follows directly from log(ab)=log(a)+log(b).
10^.3 is about the same as cube root of 10 which should be about 2.1 or something like that - 2^3 is 8, so you need a bit more than 2. 10^-4=0.0001. =>10^-3.7=2.1*0.0001 = 0.00021
I don't mean to hijack the thread, but what about 10^-3.7?
TBR says "10^-3.7 = (10^0.3)*10^-4"
What in the ****? What is the method behind that? It's nice how they don't even mention this technique but they thought it was appropriate to have a page-long table that painstakingly confirms log(ab)=log(a)+log(b) and log(a/b)=log(a)-log(b).
Wanna know a trick for this? If you're not familiar with what I call the "log trick of 3's" then read this first: http://forums.studentdoctor.net/showpost.php?p=6412828&postcount=3
So knowing that -log(3 x 10^-q) = ~ (q-1).5 such that -log(3 x 10^-5) = ~4.5
I messed around in Wolfram|Alpha one day and realized this trick works another way:
If you have an expression where 10^-q, then the trick of 3's holds, just in reverse.
10^-5 = 1 x 10^-5
10^-5.5 = ~3 x 10^-6
10^-6 = 1 x 10^-6
10^-6.5 = ~3 x 10^-7
and so on. So for a value like 10^-3.7, I would note that the decimal 7 is greater than 5, meaning the value of the mantissa is below 3, and the exponent is 10^-4. Conclusion is that 10^-3.7 = <3 x 10^-4
This should be accurate enough to identify the answer needed, if this is a terminal step in solving a problem.