Notes on significant figures and measured values of College Physics Experiments

I have to say that the expression of the effective number and measured value of college physics experiment really confused me. The teacher briefly passed the introduction. As a result, the requirements of the experimental report were strict Here according toInformation collected onlineandPersonal understandingMake a summary for later reference

Teaching materials used in our school:College physics experiment course editor in chief: Xu Taotao – Science Press

0x01 what is the significant number

https://zhuanlan.zhihu.com/p/380393523

The above article has put the number of significant figuresAddition and subtraction，Multiplication and division，Scientific counting methodThe calculation is explained to me. The summary is as follows:

1. Significant numberRound off
   (here)Five pairsperhapsFifty pairsIt refers to the first digit of 5. If yeseven numbersGive it up, if soOdd numberGo to 5 into 1 and make this odd number even

   ///////Note:In large object experimentSQL Function it seems thatRegardless of the number after 5, if it is an even number before 5, it will be rounded off, and if it is an odd number, it will be rounded into one///////

2. Multiplication, division, addition and subtraction of significant numbersTrim on resultsAll watchingOperation formulaMediumA high position in the tail(Note: the number of digits decreases gradually from left to right – ten thousand)

3. Addition and subtraction formulaMedium lookIn the formula taildigithighestResult valueTail digitMatch it
   such as520-131.4=388.6=389, whereTail highest positionyes5200, i.eBit, so the result is alsoReserved to bits

4. Multiplication and divisionMedium lookMinimum number of significant digitsResult valuesignificant digits Match it
   such as1.98x7.9=15.642=16, whereKeep the least significant digitsYes7.9, two, so the result countsKeep two significant digits

5. Scientific counting formulaLook at each valueIndex of 10Is it the same? If not, unify it. Other operations are the same as addition and subtraction

6. Compound operationParentheses, multiplication and division, addition and subtraction

In addition, there are several points for attention in the book:

1. Logarithmic functionIn the calculated resultNumber of decimal places reservedandThe real number is the same as the number of significant digits

   
   

   For example, in the first example, the real number is1.983, there are four significant digits, so the last rounding off is toFour decimal places->0.6846

2. exponential functionResults insignificant digits andThe index has the same number of digits after the decimal point(the textbook I use is written like this)

   

   The index of 10 in this example6.25, the number of digits after the decimal point is2 bits, the results will be retainedTwoSignificant digit 1.8e + 6

3. trigonometric functionResults insignificant digits andNumber of significant digits of angleagreement

   

   In this example, the angle of 30 ° 00 ‘is4 bitsSignificant numbers, the results are retainedFourSignificant digit 0.5000

4. Other functionstakeindependent variableoflast placeChange 1 to calculate the resultResulting differencesThe highest position should be reservedLast significant digit(to be honest, I haven’t seen this for a long time. I checked it online for a long time, this ghost book doesn’t give an example, it probably means the following)

   • Suppose I have a function:

     

   • Or more conveniently, we convert it into Python statements:

     

     

   • First, we pass in a value of 0.43655 to the independent variable x, and the result is0.4088509025。 Then, 0.43655 + 0.00001 = 0.43656 is passed in, that isThe last bit of the argument changes 1, we get the results0.4088646336。

   • Two resultsResulting differencesIt’s 0.0000137311. Note hereHighest positionrefer toThe first digit to make a difference from left to rightFor example, here is 0.0000137311, the fifth digit after the decimal point is the first digit causing the difference

   • Therefore, the two results we calculated should also beRounding off is reserved to the fifth decimal place, two results are obtained:

     result1 = 0.40885  
     result2 = 0.40886

   • In addition, there is another online example for reference:

     

5. aboutThe number of significant digits is infiniteValues, likeπ，e，1/3,2^{0.5}And so on, you can compareTake one more significant digitSimilarly, the intermediate process of operation can also be usedKeep one more bitTo ensure accuracy

0x02 expression of experimental measurement results

Well, the significant number is done, and we have reached another point of egg pain – the expression of the experimental measurement result. The main test isMean ± uncertaintyLet’s mainly remember this

0. College Physics ExperimentUncertaintySignificant numbers for simplicityGenerally, only1position，The first significant digit is 1 or 2Time retention2Bit (when rounding)Only advance but not retreat, not rounded). andRelative uncertaintyUsually reserved2position
1. unifiedaverage valueUnit andUncertaintyCompany
2. Use when the average result is very largeScientific counting methodExpress
3. seeUncertaintyWhich digit of the significant number is reserved, corresponding toaverage valueJust keep it to who
   such as7.5586±0.003, uncertainty0.003If the significant number is kept to the third place after the decimal point, the average value shall also be kept to the third placeThree decimal placesThat is, the result is written as7.559±0.003

After all

Today’s learning really needs to make full use of network resources There will be several big experiments to be done later. It’s time for the pain mask