Convert figures to a common unit. It doesn't matter what that unit is, but each figure should use the same one. As an example, you might say a man is 1.7 meters tall, but a 2mm ant is 0.002 meters tall.
How to Calculate Orders of Magnitude in Exponents
Converting a number to an order of magnitude displays its approximate scale and omits any absolute measurement, which means it has zero significant figures. The resulting number readily compares to other figures to estimate the magnitude of their differences. Order of magnitude uses a base10 logarithmic scale, so each step on the scale is 10 times the previous one, or 10 to the power of the magnitude. As an example, saying a man is three orders of magnitude taller than an ant means he's approximately 1,000 times taller (1, followed by three "magnitude" zeros).
Instructions


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Express each figure in scientific notation by writing it with one digit before the decimal point, followed by "x 10^n" where "n" is the number of places the decimal moved. Moving the decimal to the left results in a positive number, but moving it to the right results in a negative number. In the example, you didn't have to move the decimal for 1.7, so the n is zero, giving you "1.7 x 10^0." However, you had to move the decimal in the ant's height three places to the right, so n is negative three, giving you "2.0 x 10^3."


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Round the figure to the closest power of 10. Because we're rounding scientific notation, you must use the square root of 10 (3.16) as the rounding cutoff, instead of the arithmetic five. Using this cutoff results in a 3factor maximum scale error, instead of the arithmetic method's potential error factor of 10. In the example, both numbers are less than 3.16, so the orders of magnitude are simply 10^0 and 10^3, respectively. However, if you had the number 4.1 x 10^5, 4.1 is larger than 3.16, so round up to 10 and then move the decimal point again; therefore, the 10^5 part increments one to describe a 10^6 order of magnitude.

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Subtract the smaller magnitude exponent from the larger one to calculate the scale difference. In the example, 0 minus negative 3 calculates a difference with three orders of magnitude.

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