महत्ता का क्रम
विकिपीडिया, एक मुक्त ज्ञानकोष से
| महत्ता का क्रम |
|---|
| क्षेत्रफल |
| कोणीय वेग |
| मुद्रा |
| आंकड़े |
| घनत्व |
| ऊर्जा |
| आवृत्ति |
| लम्बाई |
| भार |
| संख्याएं |
| शक्ति |
| दबाव |
| विशिष्ट ऊर्जा घनत्व |
| विशिष्ट ऊष्मा धारिता |
| गति |
| तापमान |
| समय |
| आयतन |
| इकाइयों का रूपांतरण |
| भौतिक इकाई |
| SI |
| SI मूल इकाई |
| SI व्युत्पन्न इकाई |
| SI उपसर्ग |
| प्लैंक इकाई |
महत्ता का क्रम कहते हैं एक मानदण्ड के वर्ग को या किसी राशि की महत्ता को, जहाँ प्रत्येक वर्ग पिछले वर्ग के दृङ अनुपात में होता है । यह अनुपात प्रायः दस होता है ।
| शब्दों में |
दशमलव | दस की घात |
महत्ता का क्रम |
|---|---|---|---|
| दस हजा़रवाँ | 0.0001 | 10-4 | −4 |
| हजा़रवाँ | 0.001 | 10-3 | −3 |
| सौवाँ | 0.01 | 10-2 | −2 |
| दसवाँ | 0.1 | 10-1 | −1 |
| एक | 1 | 100 | 0 |
| दस | 10 | 101 | 1 |
| सौ | 100 | 10² | 2 |
| हजा़र | 1,000 | 10³ | 3 |
| दस हजा़र | 10,000 | 104 | 4 |
| दस लाख /मिलियन | 1,000,000 | 106 | 6 |
| अरब /बिलियन | 1,000,000,000 | 109 | 9 |
महत्ता के क्रमों का प्रयोग प्रायः बहुत लगभग के आंकलनों/तुलनाओं हेतु किया जाता है । यदि दो संख्याएं एक महत्ता के क्रम के अंतर पर हैं, तो एक संख्या दूसरी के लगभग दस गुणा के बराबर है । एसे ही यदि वे दो क्यमों का अंतर दिखाती हैं, तो वह सौ गुणा है । एक ही क्रम के दो नम्बरों में एक ही पैमाने पर स्थित होते हैं । बङी संख्या छोटी संख्या का अधिकतम दस गुणा हो सकती है । यही कारण है सार्थक संख्याओं के पीछे । जो राशि छोङ या पूर्णांकित की जाती है, वह कुल राशि के महत्ता से कुछ क्रम छोटी होती है, अतएव तुच्छ है ।
यह लेख अपनी मध्य अवस्था में है, यानि कि एक आधार है। आप इसे बढ़ाकर, अनुवाद करके, सुधार कर के विकिपीडिया की मदद कर सकते है। 
The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number. More precisely, the order of magnitude of a number can be defined in terms of the common logarithm, usually as the integer part of the logarithm, obtained by truncation. For example, 4,000,000 has a logarithm of 6.602; its order of magnitude is 6. When truncating, a number of this order of magnitude is between 106 and 107. In a similar example, "He had a seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily determined without a calculator to be 6. An order of magnitude is an approximate position on a logarithmic scale.
An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded to the nearest power of ten. For example, an order of magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. In other words; when rounding its logarithm, a number of order of magnitude 10 is in between 109.5 and 1010.4. An order of magnitude estimate is sometimes also called a zeroth order approximation.
An order of magnitude difference between two values is a factor of 10. For example, the mass of the planet Saturn is 95 times that of Earth, so Saturn is two orders of magnitude more massive than Earth.
The pages in the table at right contain lists of items that are of the same order of magnitude in various units of measurement. This is useful for getting an intuitive sense of the comparative scale of familiar objects.
अनुक्रम |
[संपादित करें] गैर दशमलव के महत्ता के क्रम
Other orders of magnitude may be calculated using bases other than 10. The different decimal numeral systems of the world use a larger base to better envision the size of the number, and have created names for the powers of this larger base. The table shows what number the order of magnitude aim at for base 10 and for base 1000000. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2 and tri- means 3, and the suffix -illion tells that the base is 1000000. But the number names billion, trillion themselves (here with other meaning than in the first chapter) are not names of the orders of magnitudes, they are names of "magnitudes", that is the numbers 1 000000 000000 etc.
| महत्ता का क्रम | is log10 of | है log1000000 of | |
|---|---|---|---|
| 1 | 10 | 1,000,000 | मिलियन |
| 2 | 100 | 1,000,000,000,000 | ट्रिलियन |
| 3 | 1000 | 1,000,000,000,000,000,000 | क्विंटिलियन |
SI units in the table at right are used together with SI prefixes, which were devised with mainly base 1000 magnitudes in mind. The IEC standard prefixes with base 1024 was invented for use in context of electronic technology.
The ancient apparent magnitudes for the brightness of stars uses the base ![\sqrt[5]{100} \approx 2.512](../../../../math/7/2/5/725de7c81fbb2af1095267fdb31e9345.png)
and is reversed. The modernized version has however turned into a logarithmic scale with non-integer values.
[संपादित करें] अत्यंत बगे संख्या
For extremely large numbers, a generalized order of magnitude can be based on their double logarithm or super-logarithm. Rounding these downward to an integer gives categories between very "round numbers", rounding them to the nearest integer and applying the inverse function gives the "nearest" round number.
The double logarithm yields the categories:
- ..., 1.0023-1.023, 1.023-1.26, 1.26-10, 10-1010, 1010-10100, 10100-101000, ...
(the first two mentioned, and the extension to the left, may not be very useful, they merely demonstrate how the sequence mathematically continues to the left).
The super logarithm yields the categories:
, or
- negative numbers, 0-1, 1-10, 10-1e10, 1e10-10^1e10, 10^1e10-10^^4, 10^^4-10^^5, etc. (see tetration)
The "midpoints" which determine which round number is nearer are in the first case:
- 1.076, 2.071, 1453, 4.20e31, 1.69e316,...
and, depending on the interpolation method, in the second case
- -.301, .5, 3.162, 1453, 1e1453, 10^1e1453, 10^^2@1e1453,... (see notation of extremely large numbers)
For extremely small numbers (in the sense of close to zero) neither method is suitable directly, but of course the generalized order of magnitude of the reciprocal can be considered.
Similar to the logarithmic scale one can have a double logarithmic scale (example provided here) and super-logarithmic scale. The intervals above all have the same length on them, with the "midpoints" actually midway. More generally, a point midway between two points corresponds to the generalised f-mean with f(x) the corresponding function log log x or slog x. In the case of log log x, this mean of two numbers (e.g. 2 and 16 giving 4) does not depend on the base of the logarithm, just like in the case of log x (geometric mean, 2 and 8 giving 4), but unlike in the case of log log log x (4 and 65536 giving 16 if the base is 2, but different otherwise).
[संपादित करें] इन्हें भी देखें
- Orders of approximation
- Powers of Ten
- Orders of magnitude (numbers)
- Big O notation
[संपादित करें] बाहरी कङियाँ
- Powers of 10, a graphic animated illustration that starts with a view of the Milky Way at 1023 meters and ends with subatomic particles at 10-16 meters.
- Orders of Magnitude - Distance
- What is Order of Magnitude?
