![]() When we convert rational numbers to decimal fractions they always produce a set of repeating digits. Thus one egg is exactly one twelfth (1/12) of a dozen, but the ratio of three inches to two inches (3 in/2 in) is not exact because we cannot measure lengths with unlimited precision. The quantity described must be inherently an integer to apply this rule. The student must be careful with these fractions. So 2/5 or 1/137 are ratios of exact integers and are also exact. Rational fractions: Any fraction made from integers is exact. The problem did not occur when computer date counters flipped to ’99, and is a dead issue when the flip to ’01. On the other hand the year 2000 computer problem (Y2K) that received so much press is a number with four significant figures. Most people will not trouble their friends with the price “One thousand nine hundred eighty seven dollars and thirty six cents” ($1987.36). If you tell a friend that you have paid $2000 dollars for a computer, there is only one significant figure in this number. ![]() Integers: When you count, the result is exact (assuming that you do not loose count). For example there are exactly 2.54 centimeters to the inch. Defined unit conversion values are also exact. = 3.14159…, the square root of 2 (= 1.4142135…) and similar numbers are also exact. Every digit you choose to display from this number is significant. This number has a mathematical definition and is exact. The number may be an Exact or Defined Number, it may be an integer, or the number could have been computed from numbers that have significant digits.ĭefined numbers: The base of the natural logarithms is e = 2.781828…. Other Numbers Having Significant Figuresĭirect measurement is not the only way a number may contain significant digits. Standard notation would not let us distinguish between the last two examples. Here are some examples.īut 4.0 x 10 3 has 2 significant figures. With the use of scientific notation every digit that appears is significant. We can use scientific notation to avoid misunderstanding. This would include all of the zeros in 0.0016 m. ![]() Zeros used as placeholders are not significant. Therefore we have only 2 significant figures. How many significant figures are there in this measurement? Clearly only the digits 1 and 6 are the actual measured values. For example, if you measure the thickness of a coin, you can write it as Only those figures or digits of a numerical quantity which are the result of actual measurement are said to be significant. After you have become familiar with the topic you may use either term. That way we may still say “digit” to draw your attention to a particular digit under discussion. In this document we will use the term significant figures to discuss the broader topic. These are sometimes called significant digits. The term significant figures actually refers to particular digits in a number.
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