DigitsTolType

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Digits TolType

This describes an alternative way for determining the tolerance type based on the number of digits.

Problem Techniques Index

PG problem file	Explanation
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "PGML.pl" ); TEXT(beginproblem());	Initialization: The tolType of type digits is built-in to MathObjects.
Context("Numeric") Context()->flags->set(tolType=>'digits', tolerance=>3, tolTruncation=>1); $answer = Real("pi");	Setup: The tolType=>'digits' switches from the default 'relative' tolerance type to the 'digits' tolerance type. The tolerance=>3 sets the number of digits to 3. The default value is the default for other tolerance types, 0.001, but any tolerance that is between 0 and 1 is converted via log10 and rounding to an integer (in this case, to 3). The tolTruncation parameter is either 1 (true) or 0 (false). Details are explained below. The tolExtraDigits parameter sets the number of extra digits for checking answers. This is explained below. The goal is that the student must enter at least the first tolerance digits correctly. The last digits that they enter might be rounded (always accepted) or truncated (only accepted if tolTruncation is true). For example, if the correct answer is e=2.7182818... and tolerance is 3, the student can answer with 2.72. Or they can answer with 2.71 if tolTruncation is true. But for example 2.7 and 2.73 are not accepted. If the student enters additional digits, the first additional tolExtraDigits digits (which has default 1) are examined in the same manner. For example, if the correct answer is pi=3.1415926... and default flag values are used, the student can answer with 3.14, 3.141, 3.142, 3.1415, and even 3.1418 since that 8 is beyond the extra digits checking. But for example 3.143 is not accepted, since the first extra digit is not right. (And if tolTruncation is false, 3.141 would not be accepted.
BEGIN_PGML This section is with [|tolTruncation|] set to true (1). The exact answer is [`\pi`]. Enter 3.14, 3.15, 3.141, 3.142 to see if it accepts the answer. [`\pi=`][_]{$answer} END_PGML	First Section: This tests the default characteristic of this answer checker. It should accept 3.14, 3.141 and 3.142 as correct, but not 3.15.
Context("Numeric"); Context()->flags->set(tolType=>'digits', tolerance=>3, tolTruncation=>0); $answer2 = Real("pi");	Second block explanation: First, reset the context with Context("Numeric") and then the set flags are set except for tolTruncation=>0.
BEGIN_PGML This section is with [|tolTruncation|] set to false (0). The exact answer is [`\pi`]. Enter 3.14, 3.15, 3.141, 3.142 to see if it accepts the answer. [`\pi=`][_]{$answer2} END_PGML	Second Section: This tests the default characteristic of this answer checker. It should accept 3.14, 3.142 as correct, but not 3.141 or 3.15.
Context("Numeric"); Context()->flags->set(tolType=>'digits', tolerance=>3, tolTruncation=>0,tolExtraDigits=>2); $answer3 = Real("3.14");	Second block explanation: First, reset the context with Context("Numeric") and then the set flags are set except for tolTruncation=>0 as well as the tolExtraDigits=>2.
BEGIN_PGML If we want to consider only answers to some number to digits. Enter 3.14, 3.15, 3.141, 3.142 to see if it accepts the answer. Enter [`\pi`] to the first 2 decimal places after the decimal point [_]{$answer3} END_PGML	Third Section: This allows only to the given number of digits (3). It should accept only 3.14 as correct.

Problem Techniques Index