Why is the order of magnitude of
5x10^-11
-10 instead of -11?
In a relative sense, 5*10^-11 is closer to 10^-10 than 10^-11, even though it is the arithmetic mean of the two. When talking about orders of magnitude, think logarithmically.
can you elaborate on the lograithmically bit u mentioned?
On a log scale, orders of magnitude (factors of ten) are equally spaced.
Log 1 = 0
Log 5 = 0.699
Log 10 = 1
Log 100 = 2
etc.
That is why 5 is "closer" to 10 than 1. logarithmically speaking?
To understand why the order of magnitude of 5x10^-11 is -10 instead of -11, we first need to understand what order of magnitude means.
The order of magnitude is a way to describe the scale or size of a number in terms of powers of 10. It gives a rough estimate of how large or small a number is.
In scientific notation, a number is written as a decimal number multiplied by 10 raised to a power. In the case of 5x10^-11, the decimal number part is 5, and the power of 10 is -11.
To determine the order of magnitude, we look at the power of 10. In this case, the power is -11. The order of magnitude is obtained by rounding the power of 10 to the nearest integer.
In rounding, we look at the digit right after the decimal point. If the digit is 5 or greater, we round up; if the digit is less than 5, we round down.
In -11, the digit right after the decimal point is 1. Since 1 is less than 5, we round down. So the order of magnitude of 5x10^-11 is -10, not -11.
To summarize, the order of magnitude is determined by rounding the power of 10 to the nearest integer. In this case, the power of 10 is -11, but since the digit after the decimal point is 1 (less than 5), we round down to -10 as the order of magnitude.