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An order of magnitude describes the rough scale of a quantity using powers of ten. Depending on the convention, it can mean the nearest power of ten or the power-of-ten decade shown in scientific notation. For nearest-power estimates, write a positive number as a × 10n: if a is below 5, use 10n; if it is 5 or higher, round to 10n+1.
What does “order of magnitude” mean?
It is a coarse way to describe how large or small a quantity is, expressed as a power of ten. It gives a useful sense of scale, not an exact value. For example, 200 is nearer 100 (102) than 1,000 (103), while 850 is nearer 1,000.
The phrase has two common uses: the nearest power of ten, and the decade or exponent in a number’s scientific notation. These usages can produce different answers near the boundary between decades, so name the convention when the distinction matters.
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How to find the nearest order of magnitude
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Write the positive value in scientific notation as a × 10n, where 1 ≤ a < 10.
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Compare the coefficient a with 5.
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If a < 5, use 10n. If a ≥ 5, use 10n+1.
This is the nearest-power convention taught by The Open University.
Examples
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200: 2 × 102. Since 2 is below 5, its nearest order is 102.
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850: 8.5 × 102. Since 8.5 is at least 5, its nearest order is 103.
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Mars’s diameter: The Open University uses 6,762 km, or 6.762 × 103 km; under the nearest-power convention, that is approximately 104 km.
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A very small distance: A Papua New Guinea Department of Education Grade 11 physics module gives an atomic-scale distance as 1.6 × 10−10 m and represents its order as 10−10 m. Orders of magnitude can therefore have negative exponents.
Why different sources may give different answers
In the exponent-only usage, the order identifies the power of ten in scientific notation. OpenStax describes 450 and 800 as having the same order because both can be written with a coefficient times 102. By contrast, the nearest-power rule rounds 850 to 103. Thus, 850 has exponent 2 in the decade usage but nearest order 103.
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| Usage | What it identifies | 850 example |
|---|---|---|
| Nearest power of ten | The closest power of ten under the coefficient threshold rule. | 103, following The Open University’s rule. |
| Scientific-notation decade | The exponent when the value is written as a coefficient times a power of ten. | Exponent 2, or the 102 decade, as in the scale usage described by OpenStax. |
If a question explicitly asks for the nearest order of magnitude, use the first convention. If it defines order as an exponent or decade, use the second.
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How orders of magnitude compare quantities
For a rough ratio, compare the powers of ten. A difference of two in the exponents corresponds to a factor of about 102, or 100. In a University of Reading example, Earth’s mass is rounded to 1025 kg and the Moon’s to 1023 kg, so Earth is roughly two orders of magnitude more massive—about 100 times by this estimate. The underlying example gives masses of 5.98 × 1024 kg and 7.35 × 1022 kg, respectively.
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For an order-of-magnitude comparison, see the University of Reading’s numbers, units and physical quantities resource.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.What an order of magnitude does not tell you
Because it deliberately removes detail, an order-of-magnitude estimate is useful for estimating scale and checking whether a result is plausible, but it is not a statement of measurement precision or uncertainty. Those require other information.
For instance, writing a length as 1,200 m does not by itself show whether the final two zeros are significant digits or merely indicate the size of the number. NIST discusses this ambiguity in its Guide to the SI, Chapter 7.
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Outbyte PC Repair FREEClear out junk files and repair common Windows errorsFree Scan →Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →The scientific-notation procedure described here applies directly to positive quantities. The cited teaching resources do not establish a shared general rule for assigning an order of magnitude to zero or negative values; the procedure is not directly defined for them as magnitudes.
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