MGMT 1000 Lecture Notes - Lecture 19: Decimal Mark
MGMT 1000 Lecture 19 Notes – Fractional Numbers
Introduction
• The representation and conversion of fractional numbers are somewhat more difficult
because there is not necessarily an exact relationship between fractional numbers in
different number bases.
• More specifically, fractional numbers that can be represented exactly in one number
base may be impossible to represent exactly in another.
• Thus, exact conversion may be impossible.
• A couple of simple examples will suffice.
• EXAMPLE
• The decimal fraction 0.110 or 1/10 cannot be represented exactly in binary form.
• There is no combination of bits that will add up exactly to this fraction.
• The binary equivalent begins 0.00011001100112.
• This binary fraction repeats endlessly with a repeat cycle of four.
• Similarly, the fraction 1/3 is not representable as a decimal value in base 10.
• In fact, we represent this fraction decimally as 0.3333333.
• As you will realize shortly, this fraction can be represented exactly in base 3 as 0.13
• Recall that the value of each digit to the left of a decimal point in base 10 has a weight
ten times that of its next right neighbor.
• This is obvious to you, since you already know that each digit represents a group of ten
objects in the next right neighbor.
• As you have already seen, the same basic relationship holds for any number base
• The weight of each digit is B times the weight of its right neighbor.
• This fact has two important implications: 1.
• If we move the number point one place to the right in a number, the value of the
number will be multiplied by the base.
• A specific example will make this obvious1390.
• 139010 is ten times as large as 139.010
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