# Difference between revisions of "Formulas: More examples"

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''"The significant figures of a number are digits that carry meaning contributing to its measurement resolution."'' (Reference: https://en.wikipedia.org/wiki/Significant_figures). | ''"The significant figures of a number are digits that carry meaning contributing to its measurement resolution."'' (Reference: https://en.wikipedia.org/wiki/Significant_figures). | ||

− | The Formulas question has no built-in function to display | + | The Formulas question has no built-in function to display values with a given number of significant figures. However, it is easy to work out this function as the following variable assignment which works with any real number: |

<pre style="font-size:113%;width: 98%;"> | <pre style="font-size:113%;width: 98%;"> | ||

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Random variables # a plus or minus sign | Random variables # a plus or minus sign | ||

# b exponent varying from -4 to 4 in steps of 0.01 | # b exponent varying from -4 to 4 in steps of 0.01 | ||

− | # rnsf random number of significant figures : 1, 2, 3, or 4 | + | # rnsf random number of significant figures: 1, 2, 3, or 4 |

a={-1,1}; | a={-1,1}; | ||

b={-4:4.01:0.01}; | b={-4:4.01:0.01}; | ||

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margin: 15px 0 15px; | margin: 15px 0 15px; | ||

"> | "> | ||

− | It is always a good idea to document your work using comments in the | + | It is always a good idea to document your work using comments in the '''Variables''' fields.</div> |

In this example, values to be rounded range from -10 000 to +10 000. In order to have the same number of values in each order of magnitude, hence a more interesting exercise, the random variable <span style="font-family:monospace;font-size:113%;">b</span> is used as a power of 10. By letting: | In this example, values to be rounded range from -10 000 to +10 000. In order to have the same number of values in each order of magnitude, hence a more interesting exercise, the random variable <span style="font-family:monospace;font-size:113%;">b</span> is used as a power of 10. By letting: | ||

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* For larger factorials, see WolframAlpha: [https://www.wolframalpha.com/input/?i=1000! 1000!] [https://www.wolframalpha.com/input/?i=(10%5E100)! 10<sup>100</sup>!] | * For larger factorials, see WolframAlpha: [https://www.wolframalpha.com/input/?i=1000! 1000!] [https://www.wolframalpha.com/input/?i=(10%5E100)! 10<sup>100</sup>!] | ||

− | <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin: | + | <div style="border:1px solid #bce8f1;border-radius:4px;padding: 0px 15px 0px; margin:30px 0 25px;"> |

<div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Example</div> | <div style="font-family:Lucida Sans Unicode;font-size:150%;color:#f98012;margin:10px 0 10px;>Example</div> | ||

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</div> | </div> | ||

</div> | </div> | ||

+ | |||

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[[Formulas_question_type|← FORMULAS QUESTION TYPE]] | [[Formulas_question_type|← FORMULAS QUESTION TYPE]] | ||

+ | |||

+ | ===In other languages=== | ||

+ | [https://docs.moodle.org/all/es/F%C3%B3rmulas:_M%C3%A1s_ejemplos Español]<br> | ||

+ | [https://docs.moodle.org/3x/fr/Formules:_Plus_d'exemples Français] |

## Latest revision as of 01:23, 14 January 2018

# Significant figures

*"The significant figures of a number are digits that carry meaning contributing to its measurement resolution."* (Reference: https://en.wikipedia.org/wiki/Significant_figures).

The Formulas question has no built-in function to display values with a given number of significant figures. However, it is easy to work out this function as the following variable assignment which works with any real number:

xr=x==0?x:round(x*pow(10,nsf-1-floor(log10(abs(x)))),0)*pow(10,-nsf+1+floor(log10(abs(x))));

where x is the number to be rounded, nsf the number of significant digits to keep and xr the resulting rounded value.

This example deals with the display of the correct answers with different numbers of significant figures.

The Formulas question should look like this:

Play it Login info *(Open in new tab: Ctrl+Shift+Click)*

This example is a significant figures drill.

General Question name! Significant figures drill Variables Random variables # a plus or minus sign # b exponent varying from -4 to 4 in steps of 0.01 # rnsf random number of significant figures: 1, 2, 3, or 4 a={-1,1}; b={-4:4.01:0.01}; rnsf={1,2,3,4}; Global variables # nx number x = ± 10^b nx=a*pow(10,b); # Rounding routine: # x number to round # nsf number of significant figures # xr rounded value of x x=nx; nsf=rnsf; xr=x==0?x:round(x*pow(10,nsf-1-floor(log10(abs(x)))),0)*pow(10,-nsf+1+floor(log10(abs(x)))); Main question Question text! Significant figures drill Part 1 Part's mark* 1 Answer type Number Answer* xr Grading criteria* Relative error < 0.0001 Part's text Number to round: {nx} Number of significant digits to keep: {ncs} Rounded number: {_0} Combined feedback For any correct response The correct answer is: {xr} For any incorrect response The correct answer is: {xr}

In the Variables fields (random, global and local), lines starting with # are treated as comments.

**Variables**fields.

In this example, values to be rounded range from -10 000 to +10 000. In order to have the same number of values in each order of magnitude, hence a more interesting exercise, the random variable b is used as a power of 10. By letting:

^{b}

with b ranging from -4 to +4 in steps of 0.01, there are one hundred random values in each order of magnitude (0.000 1 to 0.001, 0.001 to 0.01, 0.01 to 0.1, 0.1 to 1, 1 to 10, 10 to 100, 100 to 1 000 and 1 000 to 10 000), both positive and negative.

**In total, this example generates 6 408 different random questions:**

The Formulas question should look like this:

Play it Login info *(Open in new tab: Ctrl+Shift+Click)*

# Factorial

"In mathematics, the factorial of a non-negative integer , denoted by , is the product of all positive integers less than or equal to . For example,

The value of is , according to the convention for an empty product." (Reference: https://en.wikipedia.org/wiki/Factorial).

With the built-in function fact(), the Formulas question calculates factorial values up to (which would correspond to the largest number that can be handled by PHP). For larger values of , fact() returns INF for the value of .

However input (with {_0}, {_1}, etc.) is limited to a maximum value corresponding to .^{(Explain why)}

### References

- Factorials can readily be evaluated up to 170! on Google built-in calculator, under 64-bit Windows and Android: 170!

This simple example illustrates the use of the fact() function.

General Question name! Factorial - example 1 Variables Random variables n = {2:8}; m = {2:8}; Global variables x = fact(n)*fact(m); Main question Question text! Factorial - example 1 Part 1 Part's mark* 1 Answer type Number Answer* x Grading criteria* Absolute error == 0 Part's text Calculate: {n}! x {m}! = {_0} (enter value using integer format) Combined feedback For any correct response The correct answer is: {x} For any incorrect response The correct answer is: {x}

The Formulas question should look like this:

Play it Login info *(Open in new tab: Ctrl+Shift+Click)*

This slightly more elaborate example shows that the fact() function can handle large factorials and also that calculations with factorials can easily be performed using the fact() function.

General Question name! Factorial - example 2 Variables Random variables n = {0:171:1}; nn = {12:171:1}; na = {1:10}; m = {0:103:1}; Global variables x=fact(m); Main question Question text! Factorial - example 2 Part 1 Part's mark* 1 Answer type Number Answer* x Grading criteria* Relative error < 0.01 Part's text 1. Calculate: {m}! = {_0} (use scientific notation for large numbers) 2. It can easily be shown that {nn}! / {=nn-na}! = {=fact(nn)/fact(nn-na)}. Combined feedback For any correct response The correct answer is: {x} For any incorrect response The correct answer is: {x}

The Formulas question should look like this:

Play it Login info *(Open in new tab: Ctrl+Shift+Click)*