Comparison
At and above a thousand million (≥ 109), the same numerical value has two different names, depending on whether the value is being expressed in the long or short scale. Equivalently, the same name has two different numerical values depending on whether it is being used in the long or short scale.
Each scale has a logical justification to explain the use of each such differing numerical name and value within that scale. The short-scale logic is based on powers of one thousand, whereas the long-scale logic is based on powers of one million. In both scales, the prefix bi- refers to "2" and tri- refers to "3", etc. However only in the long scale do the prefixes beyond one million indicate the actual power or exponent (of 1,000,000). In the short scale, the prefixes refer to one less than the exponent (of 1,000).
The relationship between the numeric values and the corresponding names in the two scales can be described as:
| Value in Scientific notation |
Value in numerals |
Short Scale | Long Scale | ||
|---|---|---|---|---|---|
| Name | Logic | Name | Logic | ||
| 10 0 | 1 | one | one | ||
| 10 3 | 1,000 | thousand | thousand | ||
| 10 6 | 1,000,000 | million | million | ||
| 10 9 | 1,000,000,000 | billion | 1,000×1,0002 | thousand million or milliard | |
| 1012 | 1,000,000,000,000 | trillion | 1,000×1,0003 | billion | 1,000,0002 |
| 1015 | 1,000,000,000,000,000 | quadrillion | 1,000×1,0004 | thousand billion or billiard | |
| 1018 | 1,000,000,000,000,000,000 | quintillion | 1,000×1,0005 | trillion | 1,000,0003 |
| 1021 | 1,000,000,000,000,000,000,000 | sextillion | 1,000×1,0006 | thousand trillion or trilliard | |
| 1024 | 1,000,000,000,000,000,000,000,000 | septillion | 1,000×1,0007 | quadrillion | 1,000,0004 |
| etc. | etc. | To get from one named order of magnitude to the next: multiply by 1,000 |
To get from one named order of magnitude to the next: multiply by 1,000,000 |
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The root mil in "million" does not refer to the numeral "one". Rather, it refers to the Latin word for "thousand" (milia).
The relationship between the names and the corresponding numeric values in the two scales can be described as:
| Name | Short Scale | Long Scale | ||
|---|---|---|---|---|
| Value in Scientific notation |
Logic | Value in Scientific notation |
Logic | |
| million | 106 | 106 | ||
| billion | 109 | 1,000×1,0002 | 1012 | 1,000,0002 |
| trillion | 1012 | 1,000×1,0003 | 1018 | 1,000,0003 |
| quadrillion | 1015 | 1,000×1,0004 | 1024 | 1,000,0004 |
| etc. | To get from one named order of magnitude to the next: multiply by 1,000 |
To get from one named order of magnitude to the next: multiply by 1,000,000 |
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The word milliard, or its translation, is found in many European languages and is used in those languages for 109. However, it is unknown in American English, which uses billion, and not used in British English, which preferred to use thousand million before the current usage of billion. The financial term yard, which derives from milliard, is used on financial markets, as it is unambiguous, unlike billion. Likewise, many long scale countries use the word billiard (or similar) for a thousand long scale billions (i.e. 1015), and the word trilliard (or similar) for a thousand long scale trillions (i.e. 1021), etc.
Read more about this topic: Long And Short Scales
Famous quotes containing the word comparison:
“It is very important not to become hard. The artist must always have one skin too few in comparison to other people, so you feel the slightest wind.”
—Shusha Guppy (b. 1938)
“Most parents aren’t even aware of how often they compare their children. . . . Comparisons carry the suggestion that specific conditions exist for parental love and acceptance. Thus, even when one child comes out on top in a comparison she is left feeling uneasy about the tenuousness of her position and the possibility of faring less well in the next comparison.”
—Marianne E. Neifert (20th century)
“The comparison between Coleridge and Johnson is obvious in so far as each held sway chiefly by the power of his tongue. The difference between their methods is so marked that it is tempting, but also unnecessary, to judge one to be inferior to the other. Johnson was robust, combative, and concrete; Coleridge was the opposite. The contrast was perhaps in his mind when he said of Johnson: “his bow-wow manner must have had a good deal to do with the effect produced.””
—Virginia Woolf (1882–1941)