Hello. Thank you for these solutions. Please could you explain how you have come to the 4th term being ~0.15. I understand that you have gotten [3^2x10x0.12^3] however i do not understand how you have said that that expression is equal to [90×12^3×10^-6 ~ 0.15] Many thanks
3^2 = 9, so 3^2 x 10 is where we get the 90.
0.12^3 = (12 x 10^-2)^3 = 12^3 x 10^-6.
I didn’t work out the 0.15 exactly. I just worked out that the value was bigger then 0.1 and smaller than 0.2. Since we only need to be looking at the first decimal place we don’t need to get the exact answer.
Thanks for the swift reply and all of these solutions
It’s a pleasure.
Hi, thank you for the excellent work! Could you please explain how you approximated those decimal values without the use of a calculator?
Hi, glad you like it. See above, I just guessed at the 0.15, but I did work out that it was bigger than 0.1 and smaller than 0.2. Everybody knows that 12 x 12 = 144, and that 12 ‘9’s are bigger than 100. Therefore 12 x 12 x 12 x 90 is bigger than 144000 but obviously smaller than 200000. So the whole expression is a bit bigger than 0.14.
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