Transcript DECIMAL NUMBERS - Pedraza

ALEXANDER PENUELA
RAFAEL PEDRAZA RUIZ
SANTIAGO HUERTAS
SERGIO RIOS
FELIPE BARCHA
4-A
To understand decimal numbers
you must first know about
Place Value.
When we write numbers, the
position (or "place") of each
number is important.
In the number 327:
the "7" is in the Units position,
meaning just 7 (or 7 "1"s),
the "2" is in the Tens position
meaning 2 tens (or twenty),
and the "3" is in the Hundreds
position, meaning 3 hundreds.
"Three Hundred Twenty Seven"
As we move left, each position is 10 times
bigger!
From Units, to Tens, to Hundreds
... and ...
As we move right, each position is 10 times
smaller.
From Hundreds, to Tens, to Units
But what if we continue past Units?
What is 10 times smaller than Units?
1/ ths (Tenths) are!
10
But we must first write a decimal
point,
so we know exactly where the
Units position is:
"three hundred twenty seven and four tenths"
And that is a Decimal Number!
The zero and the counting numbers (1,2,3,...) make up the set of whole
numbers. But not every number is a whole number. Our decimal system lets
us write numbers of all types and sizes, using a clever symbol called the
decimal point.
As you move right from the decimal point, each place value is divided by 10.
decimal point
1 2 7 . 8 5 4
Hundreds
tens
ones
thousandths
hundredths
tenths
The decimal number can be represented by square or large
rectangles.
3
10
= 0.3
There are three different types of decimal number: exact,
recurring and other decimals.
An exact or terminating decimal is one which does not go on
forever, so you can write down all its digits. For example: 0.125
A recurring decimal is a decimal number which does go on forever,
but where some of the digits are repeated over and over again.
For example: 0.1252525252525252525... is a recurring decimal,
where '25' is repeated forever.
Other decimals are those which go on forever and don't have
digits which repeat. For example pi =
3.141592653589793238462643...
Example 1: If 58 out of 100 students in a
school are boys, then write a decimal for
the part of the school that consists of
boys.
Analysis: We can write a fraction and a
decimal for the part of the school that
consists of boys
FRACTION
DECIMAL
58/100
0.58
Answer: 0.58
Example 2:
Example 3:
Five swimmers are entered into a competition.
Four of the swimmers have had their turns. Their
scores are 9.8 s, 9.75 s, 9.79 s, and 9.81 s.
What score must the last swimmer get in order
to win the competition?
Analysis: We must order these decimals from least to
greatest. Then we must determine how the least
compares with the winning score.
Step 1: 9 . 75
9 . 79
9 . 80
9 . 81
Step 2: The least decimal is 9.75. Now we
must determine how 9.75 compares with
the winning score.
Answer: The last swimmer must get a
score less than 9.75 s in order to win.
1. Example 3: Ellen wanted to buy the following items: A DVD
player for $49.95, a DVD holder for $19.95 and a personal stereo
for $21.95. Does Ellen have enough money to buy all three items
if she has $90 with her?
Analysis: The phrase enough money tells us that we need to
estimate the sum of the three items. We will estimate the sum by
rounding each decimal to the nearest one. We must then compare
our estimated sum with $90 to see if she has enough money to buy
these items.
$49.95
$19.95
$21.95
$50.00
$20.00
$22.00
$92.00
Answer: No, because rounding each
decimal to the nearest one, we get an
estimate of $92, and Ellen only has
$90 with her.
In the 1968 Summer Olympics, Irena Szewinska of
Poland won the women´s 200 meters dash with a time
of 22.5 seconds,. In 1996, Marie-Jose Perec of France
won the event with a time of 22.12 seconds. Whose
time is faster?
Hundred
thousand
Ten
thousans
Thousans
Hundred
s
Tens
Ones
Tenths
2
2.
5
2
2.
1
Hundredths
2
Thousandths
Tenthousandths
22.50
22.12
The tens´and ones´digits are
the same.
Write a zero as a placeholder.
The tenths´digits are different.
5 > 1, so 22.50 > 22.12
Answer: Because 22.5
> 22.12, Perec´s time
is faster
Central Park, in Manhattan, New York, is one of the
world´s most famous parks. If you walked around the
entire perimeter of the 2.5 mile by 0.5 mile park,
how far would you walk?
0.5 mile
wide
2.5 mile long
Solution:
A = lw
Write formula for area of
= 2.5 (0.5) Substitute 2.5 for l and 0.5 for w.
= 1.25
Multiply.
Answer: The area of Central Park is about
1.25 square miles.
Ticket prices: The cost of 21 tickets to see Blue Man
Group is $761.25 . How much does each ticket?
You can use long division to divide a decimal by a
whole number. Divide as with whole numbers. Then
line up the decimal points in the quotient and the
dividend.
Solution: Dividing a decimal by a Whole Number
36.25
21 ) 761.25
63
131
126
52
42
105
105
0
Answer: Each ticket costs $36.25
Longest Submarine Sandwich: In 1979, Chef Franz
Eichenauer made a submarine sandwich that was
322.5 meters long. Suppose the sandwich was cut into
pieces each measured 25.8 centimeters. How many
would there be?
Solution:
1. Convert 322.5 meters to centimeters by multipliying
by 100.
322.5 x 100 = 32,250 so 322.5 m = 32,250 cm
2. To find the number of pieces, divide the
total length of the sandwich by the length of each
piece.
32,250 cm ÷ 25.8 cm = 1.250
Answer: The submarine sandwich would be
divided into 1.250 pieces.