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When I calculate Square Root of 0.9, it comes around 0.9486832980505138. Though I have heard people occasionally saying that the square root of 0.9 is 0.9 itself. Would it be correct to make a statement like this?

Thanks.

deadpool
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    If you round the result to one decimal only, that statement is not wrong. But one should at least indicate the rounding (e.g., say that the square root of $0.9$ is approximately $0.9$) – Hagen von Eitzen May 15 '16 at 15:00
  • Thanks. Yeah, it makes sense. – deadpool May 15 '16 at 15:07
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    Not the best choice of rounding, if you ask me, since $0.9^2\approx 0.8$... –  May 15 '16 at 15:07
  • Note that "square root of $0.9$ is $0.9$" implies that the square of $0.9$ is also $0.9$, while $0.9^2 = 0.81$, which is closer to $0.8$. So, one should be very accurate with rounding here. – lisyarus May 15 '16 at 15:07
  • @G.Sassatelli No, the other way around silly – Simply Beautiful Art May 15 '16 at 15:08
  • Anyone know how to say "rounded to one digit" in math form? Like some O notation or something? – Simply Beautiful Art May 15 '16 at 15:08
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    @SimpleArt I know it is the other way around. I'm just saying that it behaves badly when you backtrack, due to the fact that $1-\alpha\approx 0.1$. –  May 15 '16 at 15:15

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The point is that you rounded your answer to $0.9$

But even if you did round, it would be incorrect to say $\sqrt{0.9}=0.9$

The correct statement is that the square root of $0.9$ is approxiamately $0.9$

$$\sqrt{0.9}\approx0.9$$

Simply Beautiful Art
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