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Eliminate ambiguous or non-significant zeros by using Scientific Notation: For example, 1300 with three significant figures becomes 1.30 × 10 3. Likewise 0.0123 can be rewritten as 1.23 × 10 −2. The part of the representation that contains the significant figures (1.30 or 1.23) is known as the significand or mantissa.
{{Percentage | 1 | 40000000 | sigfig = 3 | nonscinote = y}} yields 00%; Use a prescribed number of significant figures with large percentages {{Percentage | 40000000 | 2 | sigfig = 3}} yields 2.00 × 10 9 % Use a prescribed number of significant figures with large percentages without scientific notation {{Percentage | 40000000 | 2 | sigfig = 3 ...
In scientific notation, this is written 9.109 383 56 × 10 −31 kg. The Earth's mass is about 5 972 400 000 000 000 000 000 000 kg. [21] In scientific notation, this is written 5.9724 × 10 24 kg. The Earth's circumference is approximately 40 000 000 m. [22] In scientific notation, this is 4 × 10 7 m. In engineering notation, this is written ...
5 / 3 1.6667: 4 decimal places: Approximating a fractional decimal number by one with fewer digits 2.1784: 2.18 2 decimal places Approximating a decimal integer by an integer with more trailing zeros 23217: 23200: 3 significant figures Approximating a large decimal integer using scientific notation: 300999999: 3.01 × 10 8: 3 significant figures
First-order approximation is the term scientists use for a slightly better answer. [3] Some simplifying assumptions are made, and when a number is needed, an answer with only one significant figure is often given ("the town has 4 × 10 3, or four thousand, residents"). In the case of a first-order approximation, at least one number given is exact.
A reading of 8,000 m, with trailing zeros and no decimal point, is ambiguous; the trailing zeros may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: 8.0 × 10 3 m indicates that the first zero is significant (hence a margin of 50 m) while 8.000 × 10 3 m indicates ...
To compare numbers in scientific notation, say 5×10 4 and 2×10 5, ... with the 6.2 the result of proper rounding using significant figures, ...
For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten (about 3.162). For example, the nearest order of magnitude for 1.7 × 10 8 is 8, whereas the nearest order of magnitude for 3.7 × 10 8 is 9.