question: Why do studies like Physics and Chemistry prefer significant figures over higher decimal accuracy?
comment: Because more digits doesn't mean more accuracy. If I measure that I traveled 1 meter in 3 seconds and I want to calculate my average speed, I will get 0.3333... meters/second. There are an infinite amount of digits in that number, ergo I measured this with infinite accuracy? No. Not at all. Significant figures is basically embedding additional information into the result with respect to the precision of the instruments used to take the measurement. If my length measuring device measures to the nearest tenth of a meter and my time-keeping device measures to the nearest tenth of a second, then my resulting answer will reflect that: 1.0 / 3.0 = 0.3 Because those are the only digits I can be sure about. Based on the precision of my instruments, I have no way of knowing if my distance traveled was actually 1.00 or 1.09 or if the time elapsed was 3.00 or 3.09 and those can give a variety of difference average speeds from 0.3236... to 0.363333.... The only digit common among them is 0.3 and the only digit that should be reflected in the answer.
passages: BULLET::::- There is no formal presentation of decimal addition. Students are instructed to begin by using colored pencils on 10,000 grid chart. The addition of decimals is related to students' work with whole number addition, with attention paid to place values so that students understand the reasoning behind lining up decimal points.
   In science and engineering, convention dictates that unless a margin of error is explicitly stated, the number of significant figures used in the presentation of data should be limited to what is warranted by the precision of those data. For example, if an instrument can be read to tenths of a unit of measurement, results of calculations using data obtained from that instrument can only be confidently stated to the tenths place, regardless of what the raw calculation returns or whether other data used in the calculation are more accurate. Even outside these disciplines, there is a tendency to assume that all the non-zero digits of a number are meaningful; thus, providing excessive figures may lead the viewer to expect better precision than exists.
   A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 8436 m would imply a margin of error of 0.5 m (the last significant digits are the units).
   Another issue is that knowledge of results may give information to the instructor as to ways the material can be improved. Using a teaching program on decimal arithmetic, an experienced teacher can put student mistakes into types. For example, one group of mistakes are due to the learners not understanding the rules about placement of the point in decimal multiplication. This shows where and how the learning material needs to be revised.
  
  Section::::Conscious thought not always essential.
   The rules for calculating significant figures for multiplication and division are opposite to the rules for addition and subtraction. For multiplication and division, only the total number of significant figures in each of the factors matters; the decimal place of the last significant figure in each factor is irrelevant. For addition and subtraction, only the decimal place of the last significant figure in each of the terms matters; the total number of significant figures in each term is irrelevant. However, greater accuracy will often be obtained if some non-significant digits are maintained in intermediate results which are used in subsequent calculations.
   In the special context of quoting the prices of stocks, traded almost always in blocks of 100 or more shares and usually in blocks of many thousands, stock exchanges in the United States used eighths or sixteenths of dollars, until converting to decimals between September 2000 and April 2001.
  
  Similarly, in the UK, the prices of government securities continued to be quoted in multiples of of a pound ( d or  p) long after the currency was decimalised.
  
  Section::::Mauritania and Madagascar.
   BULLET::::- The significance of trailing zeros in a number not containing a decimal point can be ambiguous. For example, it may not always be clear if a number like 1300 is precise to the nearest unit (and just happens coincidentally to be an exact multiple of a hundred) or if it is only shown to the nearest hundred due to rounding or uncertainty. Many conventions exist to address this issue, but these conventions are mostly esoteric and not understood by those who are not specialists in the subject:
   Although all decimal fractions are fractions, and thus it is possible to use a rational data type to represent it exactly, it may be more convenient in many situations to consider only non-repeating decimal fractions (fractions whose denominator is a power of ten). For example, fractional units of currency worldwide are mostly based on a denominator that is a power of ten. Also, most fractional measurements in science are reported as decimal fractions, as opposed to fractions with any other system of denominators.
   The NBS technical note also states that "Basically, integers are more convenient than expressions which include decimal parts [decimal fractions]. Furthermore, where measuring devices are used, values which represent numbered subdivisions on such instruments are more useful than values which have to be interpolated. For example, where a tape or a scale is graduated in intervals of 5, any value that represents a multiple of 5 is more "convenient" to measure or verify than one which is not. In addition, where operations involve the subdivision of quantities into two or more equal parts, any number that is highly divisible has an explicit advantage."
   Decimal numbers are an essential part of the metric system, with only one base unit and multiples created on the decimal base, the figures remain the same. This simplifies calculations. Although the Indians used decimal numbers for mathematical computations, it was Simon Stevin who in 1585 first advocated the use of decimal numbers for everyday purposes in his booklet "De Thiende" (old Dutch for 'the tenth'). He also declared that it would only be a matter of time before decimal numbers were used for currencies and measurements. His notation for decimal fractions was clumsy, but this was overcome with the introduction of the decimal point, generally attributed to Bartholomaeus Pitiscus who used this notation in his trigonometrical tables (1595).
   In Albania, grades from 4 to 10 are used, with some schools allowing decimals (up to the hundredth digit) and some others only allowing whole numbers.
   For tables with greater precision (more digits per value), higher order interpolation may be needed to get full accuracy. In the era before electronic computers, interpolating table data in this manner was the only practical way to get high accuracy values of mathematical functions needed for applications such as navigation, astronomy and surveying.
  
  To understand the importance of accuracy in applications like navigation note that at sea level one minute of arc along the Earth's equator or a meridian (indeed, any great circle) equals approximately one nautical mile ().
  
  Section::::See also.
  
  BULLET::::- Abramowitz and Stegun "Handbook of Mathematical Functions"
   Historically, the use of decimal sub-units was the exception rather than the rule. Decimalised currencies are well suited for mathematics based on a decimal system, as calculations involving currency can simply be treated as any other arithmetic equation; as the decimal system prevails today it is thus advantageous in fields such as accounting. However, historically there have been other systems that were in common use, such as the vigesimal system (base 20) that was common among ancient Mesoamerican civilizations or the sexagesimal system (base 60) used by the ancient Mesopotamians; the advantages of using a decimalised currency are less applicable.
   When a number is converted into normalized scientific notation, it is scaled down to a number between 1 and 10. All of the significant digits remain, but the place holding zeroes are no longer required. Thus 1,230,400 would become 1.2304 × 10. However, there is also the possibility that the number may be known to six or more significant figures, in which case the number would be shown as (for instance) 1.23040 × 10. Thus, an additional advantage of scientific notation is that the number of significant figures is clearer.
  
  Section::::Significant figures.:Estimated final digit(s).
   Numbers are often rounded to avoid reporting insignificant figures. For example, it would create false precision to express a measurement as 12.34525 kg (which has seven significant figures) if the scales only measured to the nearest gram and gave a reading of 12.345 kg (which has five significant figures). Numbers can also be rounded merely for simplicity rather than to indicate a given precision of measurement, for example, to make them faster to pronounce in news broadcasts.
  
  Section::::Identifying significant figures.
  
  Section::::Identifying significant figures.:Concise rules.
  
  BULLET::::- All non-zero digits are significant: 1, 2, 3, 4, 5, 6, 7, 8, 9.
   Scientists often record (rather than observe) time as decimals. For example, decimal days divides the day into 10 equal parts, and decimal years divides the year into 10 equal parts. Decimals are easier to plot than both (a) minutes and seconds, which uses the Sexagesimal numbering system, (b) hours, months and days, which has irregular month lengths. In astronomy, the so-called Julian day uses decimal days centered on noon.
  
  BULLET::::- Seconds in a decimal minute
  
  Since there are 60 seconds in a minute, a tenth part represents 60/10 = 6 seconds.
  
  BULLET::::- Minutes in a decimal hour
   Decimalisation is the conversion of a measurement system to units related by powers of 10, replacing traditional units that are related in other ways, such as those formed by successive doubling or halving, or by more arbitrary conversion factors. Units of physical measurement, such as length and mass, were decimalised with the introduction of the metric system, which has been adopted by almost all countries with the prominent exception of the United States. Thus a kilometre is 1000 metres, while a mile is 1,760 yards. Electrical units are decimalised worldwide. Common units of time remain undecimalised; although an attempt was made during the French revolution, this proved to be unsuccessful and was quickly abandoned.
   The typical arithmetic precision of a slide rule is about three significant digits, compared to many digits on digital calculators. As order of magnitude gets the greatest prominence when using a slide rule, users are less likely to make errors of false precision.
   Another common type of decimal time is decimal hours. In 1896, Henri de Sarrauton of the Oran Geographical Society proposed dividing the 24 hours of the day each into 100 decimal minutes, and each minute into 100 decimal seconds. Although endorsed by the Bureau des Longitudes, this proposal failed, but using decimal fractions of an hour to represent the time of day instead of minutes has become common.
   The University of Saskatchewan and University of Regina both use a percentage grade system, universal across faculties and departments.
  
  Section::::North America.:Mexico.
  
  Mexican schools use a scale from 0 to 10 to measure students' scores. Since decimal scores are common, a scale from 0 to 100 is often used to remove the decimal point.
   Many of the advantages claimed for the metric system could be realized by any consistent positional notation.
  
  Dozenal advocates say duodecimal has several advantages over decimal, although the switching cost appears to be high.
  
  Section::::Mathematics.
  
  Section::::Mathematics.:Base of the numeral system.
   Decimalised currencies also have disadvantages. The principal advantage of most non-decimal currencies is that they are more easily divided, particularly by numbers such as 3 and 8, than decimal currencies, due to being based upon conversion values that have a large number of factors. A currency with a 100:1 ratio divisible neither into 3 nor into 8, and furthermore 100 may be an uncomfortably large number for some poorly educated people to deal with. For example, one-third of an Austrian Gulden (of 60 Kreuzer) was 20 Kreuzer while a third of a dollar is 33. cents. This divisibility is useful when trading and when sharing out sums of money. For these reasons, many states chose in the past to adopt non-decimal currencies based on divisions into sub-units such as 12 or 20, sometimes with more than one tier of sub-units.
   It is also possible that the overall length of a ruler may not be accurate to the degree of the smallest mark, and the marks may be imperfectly spaced within each unit. However assuming a normal good quality ruler, it should be possible to estimate tenths between the nearest two marks to achieve an extra decimal place of accuracy. Failing to do this adds the error in reading the ruler to any error in the calibration of the ruler.
  
  Section::::Estimation.
   BULLET::::- In many long-time metric countries, when non-metric units are used, it is often to give rough estimates in a short form, while accurate measures always are metric, e.g., "6 feet" may feel less exact and shorter to say than "1.8 metres" or "180 cm". Measurement tools for inches are generally rare to find there, only on the other side of some carpenter's rulers, and may present a variation between national legacy inches and British/US inches, easily causing significant measurement errors if used.
   ISO 5725-1 and VIM also avoid the use of the term "bias", previously specified in BS 5497-1, because it has different connotations outside the fields of science and engineering, as in medicine and law.
  
  Section::::In binary classification.
  
presuppositions: More decimals means more accuracy. Higher decimals means greater accuracy to significant figures.
corrections: More digits doesn't always mean more accuracy. Higher decimals doesn't necessarily mean greater accuracy than significant figures.
raw_presuppositions: More decimals means more accuracy. Higher decimals means greater accuracy to significant figures.
raw_corrections: More digits doesn't always mean more accuracy. Higher decimals doesn't necessarily mean greater accuracy than significant figures.