How to convert decimal fractions to binary in a more attractive way

We all know how to convert decimal integral numbers to binary (don't we?) by the simple method of dividing succesively by 2 and using the remainders but what happens when we are trying to convert a decimal number which has a fractional part?

First we can see that it is obvious that the integral part of a decimal number will always be represented by an integral binary (with no fractional part) while the fractional part of a decimal number will always be represented by a fractional part of a binary number (with no integral part). An integral number will be integral in any integral base and a fractional number will be fractional in any integral base. This means we can split a decimal number into its integral and fractional parts, convert them separately to binary and add them up again in binary. This means we can forget about the integral part and concentrate on converting the fractional part. Some decimal fractions may convert into binary exactly (like .5625) but others may not (like .5624) and we may get an infinite number of binary digits in the binary fraction.

One way of converting a decimal fraction to binary fraction is to first multiply it by a power of 2 so that it becomes an integral number, then convert to binary and then divide by the same power of 2 (which now just means displacing the binary point to the left).

- Convert .5625 to binary
- Multiply .5625 * 2^10 = 576
- Convert 576 to binary = 1001000000
- Divide 1001000000 / 2^10 = .1001000000
(Same thing, more precision)

- Convert .5624 to binary
- Multiply .5624 * 2^20 = 589719.1424
- Convert 589719 to binary = 10001111111110010111
- Divide 10001111111110010111 / 2^20 = .10001111111110010111 (The more precision you want, the higher the power...

...Binary Number System:
Conversion of Decimal number to Binary number:
Set up the problem. For this example, let's convert the decimal number 15610 to binary.
Write the decimal number as the dividend inside an upside-down "long division" symbol.
Write the base of the destination system (in our case, "2" for binary) as the divisor outside the curve of the division symbol....

...Literature Cited listing at the back of this
plan.
3.1
Principles of Watershed Protection
•
Forested watersheds generally yield higher quality water than non-forested cover types. Urban,
suburban and agricultural land uses all contribute in some way to lowered water quality.
•
Uncontrolled human activities on water supply watersheds represent a major source of potential
contamination. Efficient and effective water quality protection on both filtered and...

...Decimalsdecimals
The decimal numeral system (also called
base ten or occasionally denary) has ten
as its base.
It is the numerical base most widely used
by modern civilizations.
Decimals also refer to decimalfractions.
To understand decimal numbers you must
first know about Place Value.
When we write numbers, the position (or
"place") of each number is important.
History of...

...Fraction (mathematics)
A fraction (from Latin: fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: \tfrac{1}{2} and 17/3) consists of an integer numerator, displayed...

...Fractions
The problem here is to add and |
These two fractions do not have the same denominators (lower numbers), so we must first find a common denominator of the two fractions, before adding them together.
For the denominators here, the 8 and 14, a common denominator for both is 56.
With the common denominator, the
becomes a
and the
becomes a
So now our addition problem becomes this...
The problem here is to add and |
Since these...

...are valuable but neither rare or imperfectly imitable.(Amit,2001)
The resource-based theory is based on the assumption that firms are fundamentally heterogeneous regarding their resources and internal competencies. This debates with the problem of how firms can exploit their internal resource base and capabilities to obtain sustained competitive advantages. The articles also provides a precise distinction between the intrinsic causal ambiguity associated with a particular...

...PROPOSAL ON HOW TO MAKE IRKUTSK CITY MOREATTRACTIVE AS A TOURISTIC CITY
A Proposal Submitted to
The Irkutsk department of tourism
March 30, 2012
Prepared by
Tatiana Peskova
Snezhana Polozova
Maria Selezneva
TABLE OF CONTENT
TABLE OF CONTENT 2
EXECUTIVE SUMMARY 3
INTRODUCTION 4
THE PROBLEM 4
THE BACKGROUND 5
PROPOSED SOLUTION 6
RECOMMENDED COURSE OF ACTIONS 7
REFERENCE LIST 9
EXECUTIVE SUMMARY
This paper entitled...

...as teachers and administrators. This approach has many implications for the design of curriculum, course content, and interactivity of courses.
For instance, a student-centred course may address the needs of a particular student audience to learn how to solve some job-related problems using some aspects of mathematics. In contrast, a course focused on learning mathematics might choose areas of mathematics to cover and methods of teaching which would be considered irrelevant by...

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