- #1

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**"to the nearest order of magnitude."**

Just what is meant when a question asks to do your answer "to the nearest order of magnitude."

- Thread starter Beer w/Straw
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- #1

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Just what is meant when a question asks to do your answer "to the nearest order of magnitude."

- #2

- 611

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Hi,

for e.g., 1 order of magnitude : 10.

2 order of magnitude: 100.

Also for e.g., x=9.3, then x is 1 order of magnitude.

So nearest order of magnitude might be something like rounding off !

- #3

mathman

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It is rounding off, but in a logarithmic rather than linear scale.

- #4

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The question and answer would make a good addition to the PF Library Items.

- #5

mathman

Science Advisor

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Just to clarify my answer precisely. The logarithmic scale would be to base 10, not natural.

- #6

- 611

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Yes i think it should be base 10..(from wiki)

- #7

- 12,115

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I would phrase things a little differently, and say to round to the nearest power of 10. For example, 1, 10, 100, ... or 0.1, 0.01,....

Examples:

680 meters gets rounded to 1000 meters.

2350 m also gets rounded to 1000 m.

0.9 m → 1 m

0.2 m → 0.1 m

A value like 4 m is tricky. While closer to 1 m than 10 m on a linear scale, it is actually closer to 10 m on a logarithmic scale. So it becomes 10 m, to the nearest order of magnitude.

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