Transcript Decimal Number System (1)

The Decimal Number System
 Decimal Number System
 Decimal Fractions
 Rounding Whole Numbers
 Rounding Non-whole Numbers
Decimal Numbers (cont.)
 Signed Numbers
 Addition And Subtraction
 Multiplication And Division
 Mathematical Expressions And Terms
Decimal Number System (1)
 Decimal means base ten
 The decimal system uses 10 digits:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9
 Each position in a number has a place value.
Decimal Number System (2)
 The MSD is leftmost nonzero digit.
 The MSD (most significant digit) has the greatest
effect on the value of the number.
 The least significant digit (LSD) is the digit with a
place value that has the smallest effect upon the
number's value. The LSD is at the right of a number.
 The LSD can be (and often is) zero.
Decimal Fractions (1)
 A fraction has two numbers (1/2). The numerator,
and the denominator.
 In a fraction, the numerator is divided by the
denominator.
 A fraction whose denominator is 10 or a power of
ten is known as a decimal fraction.
 To convert from a decimal fraction to a decimal
number, determine the value of the denominator and
place the LSD of the numerator in that position.
Rounding Whole Numbers (1)
 Rounding numbers to the nearest place value, which
becomes the new LSD, is a common method used to
simplify calculations.
 A general rule is if the digit to the right of the new
LSD is 4 or smaller (4, 3, 2, 1, 0), replace the digits to
the right of the new LSD with zeros.
 if the digit to the right of the new LSD is 5 or greater
(5, 6, 7, 8, 9), increase the new LSD by one and
replace the digits to the right of the new LSD with
zeros.
Rounding Whole Numbers
(2)
 In order to maintain the desired number of
significant digits, truncate the number at the new LSD
and add a times value or words so that the number of
significant digits is correct.
 If you want 3 significant digits, then: 654321 becomes
654000 which becomes 654 x 1000 or 654 thousand.
 3456789 becomes 3460000 which becomes 346 x
10000 or 346 ten thousands
Rounding Non-whole Numbers
 Use the same system as above to round
decimal numbers. The number of significant
digits is independent of decimal place. If you
want 4 significant digits, 0.00345678 becomes
0.003457 and 876.54321 becomes 876.5
Signed Numbers
 Numbers can have + or - signs. These numbers are
called signed numbers.
 Some common symbols are < (less than) and >
(greater than). For example, 1 < 2 (1 is less than 2)
and 6.7 > 5.2 (6.7 is greater than 5.2).
 If the value of the number is used without regard to
the sign, then that value is called the absolute value.
The absolute value of -17 and 17 is +17. The
magnitude of a number ignores the sign.
Addition And Subtraction
(1)
 The signs + and - indicate the sign of a
number. They also indicate addition and
subtraction. The magnitude of the number is the
number without a sign.
 Adding two or more positive numbers involves
just adding the magnitudes and using a plus
(+) sign on the result.
Addition And Subtraction
(2)
 Adding two or more negative numbers involves just
adding the magnitudes and using a negative sign (-)
on the result.
 Adding numbers with opposite signs is a different
process. Add together all the positive numbers and
then add together all the negative numbers. Subtract
the absolute value of the lesser number from the
absolute value of the greater number and place the
sign of the largest number before the answer.
Addition And Subtraction
(3)
 The process of subtraction involves the first
number called the minuend, minus the second
number, called the subtrahend. The answer is
called the difference. The rule in subtraction is
to change the sign of the subtrahend and add
as before.
Multiplication And Division
(1)
 Symbols are used to denote multiplication and
division. The symbol for multiplication is x or
* or no operator given before a left paren (or a
letter).
 Division symbols are  or / or a fraction line.
Division always means to take reciprocal and
then multiply.
Multiplication And Division
(2)
 Multiplying or dividing signed numbers requires a
method of determining the sign of the result.
 Positive signed numbers multiplied or divided will
always result in a positive answer.
 Multiplying or dividing an even number of negative
numbers will result in a positive answer. Multiplying
or dividing an odd number of negative numbers will
result in a negative answer.
Mathematical Expressions
And Terms (1)
 A mathematical term is a number preceded by
a + or - sign.
 An expression is a group of two or more
terms.
 Mathematical expressions are often grouped
together in parenthesis ( ), brackets [ J, or
braces { }. All of these are types of
parentheses.
Mathematical Expressions
And Terms (2)
 Use the mnemonic Please Excuse My Dear Aunt Sally to
remember the order of operations.
 A mathematical expression using these groupings
must be solved by first performing the calculations
within each set of parentheses, brackets, or braces.
 Next do any exponents (which includes powers and trig
functions).
 Change any number after division sign to the
reciprocal and change  to x since division is just a
special type of multiplication.
Mathematical Expressions
And Terms (3)
 Next do all multiplications (including those from
reciprocals of division).
 Lastly, do all additions and subtractions.
The End