# To the nearest order of magnitude.

#### Beer w/Straw

"to the nearest order of magnitude."

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

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#### Rajini

Re: words

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 !

#### mathman

Re: words

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

#### pallidin

Re: words

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

#### mathman

Re: words

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

#### Rajini

Re: words

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

#### Redbelly98

Staff Emeritus
Homework Helper
Re: words

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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