IsExact()

oT = StzNumberQ("1")
oT.Divide("3")
? oT.Content()
? oT.IsExact()
? oT.WhyNotExact()

oM = StzNumberQ("0.1")
oM.MultiplyBy("3")
? oM.Content()
? oM.IsExact()
? 0.1 * 3 = 0.3

oS = StzNumberQ("0.1")
oS.Add("0.2")
? oS.Content()
? oS.IsExact()
? oS.Representation()

oQ = StzNumberQ("1/3")
? oQ.Representation()
? oQ.IsExact()
oQ.Add("2/3")
? oQ.Content()
? oQ.Same(1)

oMix = new stzNumber("1/4")
oMix.Add("0.25")
# a quarter plus 0.25 is a half
? oMix.Content()
# ...as a fraction, not 0.5
? oMix.Representation()
# ...and exactly
? oMix.IsExact()
# ...which is what lets a third survive meeting a decimal
? (new stzNumber("1/3")).AddQ("0.5").Content()

tiny = number("1e-20")
oTiny = new stzNumber(tiny)
# the digits are kept
? oTiny.Content()
# ...so the value is still positive
? oTiny.NumericValue() > 0
# ...and scaling it back recovers 1
? oTiny.NumericValue() * number("1e20")
oTiny.MultiplyBy(2)
# it is exact, because the content is a plain decimal the exact path can use
? oTiny.Content()
# ...and says so
? oTiny.IsExact()

oBig = new stzNumber("1/99999999999999999999999999999999")
# a 32-digit denominator survives construction
? oBig.Content()
# ...and reports as a fraction
? oBig.Representation()
oSum = new stzNumber("1/99999999999999999999999999999999")
oSum.Add("1/99999999999999999999999999999999")
# adding it to itself doubles the numerator
? oSum.Content()
# ...exactly
? oSum.IsExact()
# a fraction that reduces from big parts still lands on the small answer
? (new stzNumber("123456789012345678901234567890/246913578024691357802469135780")).Content()

# 1 / 8 is 0.125
? (new stzNumber("1")).DivideQ("8").Content()
# 0.1 / 4 is 0.025
? (new stzNumber("0.1")).DivideQ("4").Content()
# 10 / 4 is 2.5
? (new stzNumber("10")).DivideQ("4").Content()
# 22 / 5 is 4.4
? (new stzNumber("22")).DivideQ("5").Content()
oThird = new stzNumber("1")
oThird.Divide("3")
# 1 / 3 does NOT claim to be exact
? oThird.IsExact()
# ...and says why
? StzFindFirst("does not terminate", oThird.Why()) > 0

# an exact product knows it
? (new stzNumber("19.99")).MultiplyByQ("0.15").IsExact()
# ...with nothing to explain
? (new stzNumber("19.99")).MultiplyByQ("0.15").Why()
# a big-integer sum knows it
? (new stzNumber("9007199254740992")).AddQ(1).IsExact()
oSqrt = new stzNumber("2")
oSqrt.SquareRoot()
# a square root does not pretend
? oSqrt.IsExact()
# ...and names the reason
? StzFindFirst("no exact decimal result", oSqrt.Why()) > 0
# IsApproximate is its mirror
? oSqrt.IsApproximate()
# Exactness() reports the register
? oSqrt.Exactness()

oThird = new stzNumber("1/3")
oThird.Add("2/3")
# a third plus two thirds is ONE
? oThird.Content()
# ...exactly
? oThird.IsExact()
# ...and equals the number 1
? oThird.Same(1)
# a third plus a sixth
? (new stzNumber("1/3")).AddQ("1/6").Content()
# a half less a third
? (new stzNumber("1/2")).SubtractQ("1/3").Content()
# two thirds of three quarters
? (new stzNumber("2/3")).MultiplyByQ("3/4").Content()
# a half divided by a quarter is two
? (new stzNumber("1/2")).DivideQ("1/4").Content()
# every one of those is exact
? (new stzNumber("2/3")).MultiplyByQ("3/4").IsExact()
# a third times three is one
? (new stzNumber("1/3")).MultiplyByQ(3).Content()
# ...and adding zero changes nothing
? (new stzNumber("1/3")).AddQ(0).Content()