My instances represent IEEE-754 floating-point double-precision numbers. They have about 16 digits of accuracy and their range is between plus and minus 10^307. Some valid examples are:

8.0 13.3 0.3 2.5e6 1.27e-30 1.27e-31 -12.987654e12

Mainly: no embedded blanks, little e for tens power, and a digit on both sides of the decimal point. It is actually possible to specify a radix for Squeak Float constants. This is great for teaching about numbers, but may be confusing to the average reader:

3r20.2 --> 6.66666666666667
8r20.2 --> 16.25

If you don't have access to the definition of IEEE-754, you can figure out what is going on by printing various simple values in Float hex. It may help you to know that the basic format is...
sign 1 bit
exponent 11 bits with bias of 1023 (16r3FF) to produce an exponent
in the range -1023 .. +1024
- 16r000:
significand = 0: Float zero
significand ~= 0: Denormalized number (exp = -1024, no hidden '1' bit)
- 16r7FF:
significand = 0: Infinity
significand ~= 0: Not A Number (NaN) representation
mantissa 53 bits, but only 52 are stored (20 in the first word, 32 in the second). This is because a normalized mantissa, by definition, has a 1 to the right of its floating point, and IEEE-754 omits this redundant bit to gain an extra bit of precision instead. People talk about the mantissa without its leading one as the FRACTION, and with its leading 1 as the SIGNFICAND.

The single-precision format is...
sign 1 bit
exponent 8 bits, with bias of 127, to represent -126 to +127
- 0x0 and 0xFF reserved for Float zero (mantissa is ignored)
- 16r7F reserved for Float underflow/overflow (mantissa is ignored)
mantissa 24 bits, but only 23 are stored
This format is used in FloatArray (qv), and much can be learned from the conversion routines, Float asIEEE32BitWord, and Float class fromIEEE32Bit:.

Thanks to Rich Harmon for asking many questions and to Tim Olson, Bruce Cohen, Rick Zaccone and others for the answers that I have collected here.

	comparing
	< <= = > >= closeTo: hash ~=

	converting
	adaptToFraction:andSend: adaptToInteger:andSend: asApproximateFraction asFloat asFraction asIEEE32BitWord asTrueFraction degreesToRadians isInf radiansToDegrees

	copying
	deepCopy shallowCopy veryDeepCopyWith:

	mathematical functions
	arcCos arcSin arcTan arcTan: cos degreeCos degreeSin exp floorLog: ln log raisedTo: reciprocalFloorLog: reciprocalLogBase2 safeArcCos sin sqrt tan timesTwoPower:

	printing
	absByteEncode:base: absPrintExactlyOn:base: absPrintOn:base: byteEncode:base: hex printOn:base:

	private
	absPrintOn:base:digitCount:

	testing
	hasContentsInExplorer isFloat isInfinite isLiteral isNaN isPowerOfTwo isZero sign

	truncation and round off
	exponent fractionPart integerPart reduce rounded significand significandAsInteger truncated

	constants
	e halfPi infinity nan negativeZero pi

	instance creation
	fromIEEE32Bit: readFrom:

	plugin generation
	ccg:emitLoadFor:from:on: ccg:generateCoerceToOopFrom:on: ccg:generateCoerceToValueFrom:on: ccg:prolog:expr:index: ccgCanConvertFrom: ccgDeclareCForVar:

	arithmetic	top
	* Primitive. Answer the result of multiplying the receiver by aNumber. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	+ Primitive. Answer the sum of the receiver and aNumber. Essential. Fail if the argument is not a Float. See Object documentation whatIsAPrimitive.
	- Primitive. Answer the difference between the receiver and aNumber. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	/ Primitive. Answer the result of dividing receiver by aNumber. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	abs This is faster than using Number abs.
	negated Answer a Number that is the negation of the receiver.
	reciprocal Answer 1 divided by the receiver. Create an error notification if the receiver is 0.

	comparing	top
	< Primitive. Compare the receiver with the argument and return true if the receiver is less than the argument. Otherwise return false. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	<= Primitive. Compare the receiver with the argument and return true if the receiver is less than or equal to the argument. Otherwise return false. Fail if the argument is not a Float. Optional. See Object documentation whatIsAPrimitive.
	= Primitive. Compare the receiver with the argument and return true if the receiver is equal to the argument. Otherwise return false. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	> Primitive. Compare the receiver with the argument and return true if the receiver is greater than the argument. Otherwise return false. Fail if the argument is not a Float. Essential. See Object documentation whatIsAPrimitive.
	>= Primitive. Compare the receiver with the argument and return true if the receiver is greater than or equal to the argument. Otherwise return false. Fail if the argument is not a Float. Optional. See Object documentation whatIsAPrimitive.
	closeTo: are these two numbers close?
	hash Hash is reimplemented because = is implemented. Both words of the float are used; 8 bits are removed from each end to clear most of the exponent regardless of the byte ordering. (The bitAnd:'s ensure that the intermediate results do not become a large integer.) Slower than the original version in the ratios 12:5 to 2:1 depending on values. (DNS, 11 May, 1997)
	~= Primitive. Compare the receiver with the argument and return true if the receiver is not equal to the argument. Otherwise return false. Fail if the argument is not a Float. Optional. See Object documentation whatIsAPrimitive.

	converting	top
	adaptToFraction:andSend: If I am involved in arithmetic with a Fraction, convert it to a Float.
	adaptToInteger:andSend: If I am involved in arithmetic with an Integer, convert it to a Float.
	asApproximateFraction Answer a Fraction approximating the receiver. This conversion uses the continued fraction method to approximate a floating point number.
	asFloat Answer the receiver itself.
	asFraction
	asIEEE32BitWord Convert the receiver into a 32 bit Integer value representing the same number in IEEE 32 bit format. Used for conversion in FloatArrays only.
	asTrueFraction Answer a fraction that EXACTLY represents self, a double precision IEEE floating point number. Floats are stored in the same form on all platforms. (Does not handle gradual underflow or NANs.) By David N. Smith with significant performance improvements by Luciano Esteban Notarfrancesco. (Version of 11April97)
	degreesToRadians Answer the receiver in radians. Assumes the receiver is in degrees.
	isInf simple, byte-order independent test for +/- Infinity
	radiansToDegrees Answer the receiver in degrees. Assumes the receiver is in radians.

	copying	top
	deepCopy Answer a copy of the receiver with its own copy of each instance variable.
	shallowCopy Answer a copy of the receiver which shares the receiver's instance variables.
	veryDeepCopyWith: Return self. Do not record me.

	mathematical functions	top
	arcCos Answer the angle in radians.
	arcSin Answer the angle in radians.
	arcTan Answer the angle in radians. Optional. See Object documentation whatIsAPrimitive.
	arcTan: Answer the angle in radians. Optional. See Object documentation whatIsAPrimitive.
	cos Answer the cosine of the receiver taken as an angle in radians.
	degreeCos Answer the cosine of the receiver taken as an angle in degrees.
	degreeSin Answer the sine of the receiver taken as an angle in degrees.
	exp Answer E raised to the receiver power. Optional. See Object documentation whatIsAPrimitive.
	floorLog: Answer the floor of the log base radix of the receiver.
	ln Answer the natural logarithm of the receiver. Optional. See Object documentation whatIsAPrimitive.
	log Answer the base 10 logarithm of the receiver.
	raisedTo: Answer the receiver raised to aNumber.
	reciprocalFloorLog: Quick computation of (self log: radix) floor, when self < 1.0. Avoids infinite recursion problems with denormalized numbers
	reciprocalLogBase2 optimized for self = 10, for use in conversion for printing
	safeArcCos Answer the angle in radians.
	sin Answer the sine of the receiver taken as an angle in radians. Optional. See Object documentation whatIsAPrimitive.
	sqrt Answer the square root of the receiver. Optional. See Object documentation whatIsAPrimitive.
	tan Answer the tangent of the receiver taken as an angle in radians.
	timesTwoPower: Primitive. Answer with the receiver multiplied by 2.0 raised to the power of the argument. Optional. See Object documentation whatIsAPrimitive.

	printing	top
	absByteEncode:base: Print my value on a stream in the given base. Assumes that my value is strictly positive; negative numbers, zero, and NaNs have already been handled elsewhere. Based upon the algorithm outlined in: Robert G. Burger and R. Kent Dybvig Printing Floating Point Numbers Quickly and Accurately ACM SIGPLAN 1996 Conference on Programming Language Design and Implementation June 1996. This version performs all calculations with Floats instead of LargeIntegers, and loses about 3 lsbs of accuracy compared to an exact conversion.
	absPrintExactlyOn:base: Print my value on a stream in the given base. Assumes that my value is strictly positive; negative numbers, zero, and NaNs have already been handled elsewhere. Based upon the algorithm outlined in: Robert G. Burger and R. Kent Dybvig Printing Floating Point Numbers Quickly and Accurately ACM SIGPLAN 1996 Conference on Programming Language Design and Implementation June 1996. This version guarantees that the printed representation exactly represents my value by using exact integer arithmetic.
	absPrintOn:base: Print my value on a stream in the given base. Assumes that my value is strictly positive; negative numbers, zero, and NaNs have already been handled elsewhere. Based upon the algorithm outlined in: Robert G. Burger and R. Kent Dybvig Printing Floating Point Numbers Quickly and Accurately ACM SIGPLAN 1996 Conference on Programming Language Design and Implementation June 1996. This version performs all calculations with Floats instead of LargeIntegers, and loses about 3 lsbs of accuracy compared to an exact conversion.
	byteEncode:base: Handle sign, zero, and NaNs; all other values passed to absPrintOn:base:
	hex If ya really want to know...
	printOn:base: Handle sign, zero, and NaNs; all other values passed to absPrintOn:base:

	private	top
	absPrintOn:base:digitCount: Print me in the given base, using digitCount significant figures.

	testing	top
	hasContentsInExplorer
	isFloat Overridden to return true in Float, natch
	isInfinite Return true if the receiver is positive or negative infinity.
	isLiteral Answer whether the receiver has a literal text form recognized by the compiler.
	isNaN simple, byte-order independent test for Not-a-Number
	isPowerOfTwo Return true if the receiver is an integral power of two. Floats never return true here.
	isZero
	sign Answer 1 if the receiver is greater than 0, -1 if less than 0, else 0. Handle IEEE-754 negative-zero by reporting a sign of -1

	truncation and round off	top
	exponent Primitive. Consider the receiver to be represented as a power of two multiplied by a mantissa (between one and two). Answer with the SmallInteger to whose power two is raised. Optional. See Object documentation whatIsAPrimitive.
	fractionPart Primitive. Answer a Float whose value is the difference between the receiver and the receiver's asInteger value. Optional. See Object documentation whatIsAPrimitive.
	integerPart Answer a Float whose value is the receiver's truncated value.
	reduce If self is close to an integer, return that integer
	rounded Answer the integer nearest the receiver.
	significand
	significandAsInteger
	truncated Answer with a SmallInteger equal to the value of the receiver without its fractional part. The primitive fails if the truncated value cannot be represented as a SmallInteger. In that case, the code below will compute a LargeInteger truncated value. Essential. See Object documentation whatIsAPrimitive.

	class initialization	top
	initialize Float initialize

	constants	top
	e Answer the constant, E.
	halfPi
	infinity Answer the value used to represent an infinite magnitude
	nan Answer the canonical value used to represent Not-A-Number
	negativeZero
	pi Answer the constant, Pi.

	instance creation	top
	fromIEEE32Bit: Convert the given 32 bit word (which is supposed to be a positive 32bit value) from a 32bit IEEE floating point representation into an actual Squeak float object (being 64bit wide). Should only be used for conversion in FloatArrays or likewise objects.
	readFrom: Answer a new Float as described on the stream, aStream.

	plugin generation	top
	ccg:emitLoadFor:from:on:
	ccg:generateCoerceToOopFrom:on:
	ccg:generateCoerceToValueFrom:on:
	ccg:prolog:expr:index:
	ccgCanConvertFrom:
	ccgDeclareCForVar: