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Number Sense:
DecimalsHow Do Stockholders Use Math?
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Decimals: Rounding
We round numbers when we only need a reasonableapproximation, or to keep numbers significant.
If 3 people split a pizza, each person gets:
0.333333333333. . . . of the pizza.
tenths
hundredths
thousandths millionths
billionths
trillionths
When do we stop?
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We can round two different ways:1) To a specific place value,
2) To a certain number of signif icant figures.
4625.91738
To the nearest 100
6
24600.00000
4600
or
5) Get rid of zeroes at the end.
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We can round two different ways:2) To a certain number of signif icant figures.
4625.91738
To 3 sig. fig.?
2
54630.00000
4630
5) Get rid of zeroes at the end.
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We can round two different ways:2) To a certain number of signif icant figures.
0.00000471
To 1 sig. fig.?
470.00000500
0.000005
5) Get rid of zeroes at the end.
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4
Decimals: Addition &
SubtractionWhen adding and subtracting decimalsyou must always line up the decimals!
13.7 + 0.78 13.7+ 0.78
4.9 - 2.624.9 - 2.62 Decimals lined up.And they wil l be in the answer too!
0 Add azero ifneeded.
. 841 1
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Decimals: Addition &
SubtractionWhen adding and subtracting decimalsyou must always line up the decimals!
13.7 + 0.78
4.9 - 2.62
4.9- 2.62
Decimals lined up.
And they wil l be in the answer too!
0Add azero ifneeded.
.
8 10
822
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- 105 m
Negative NumbersNegat ive numbers do not actual ly mean less than zero, in theway that we think about counting.
Instead, they are like an opposite to posit ives.
420 m
- 390 m
Where do we measure height from?
sea level +
You cant have less than zero pizzas or cookies!
opposite directions!one is positi ve,
the other is negative
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Negative NumbersOr what about kicking a bal l?
+ 3 m
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Negative NumbersOr what about kicking a bal l a little harder?
+ 4 m
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Negative NumbersOr what about kicking a ball too hard?
- 4 m
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Adding Negative
NumbersTo add, we must first decide what combination of
numbers we have.
2nd number
1st numberpositive negative
positive + / + + / -
negative - / + - / -
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Adding Negative
NumbersDepending on the combination we will do slightly
different things to reach the answer.
2nd number
1st numberpositive negative
positive add the numbers, keepthe positive sign (+)find the difference,keep the sign of the
larger value
negativefind the difference,keep the sign of the
larger value
add the numbers, keepthe negative sign (-)
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Subtracting Negative
NumbersRemember, negative numbers are. . .
OPPOSITES!We can use this to our advantageWhats the opposite, of the opposite?
THE SAME!
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Subtracting Negative
NumbersChange the operation, AND change the sign!
OPPOSITES!(-4)
Whats the opposite,of the opposite?
THE SAME!
- (+4)+
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05 10 15 20 25 30-5-10-15-20-25-30
+-Add a positi ve
0
5 10 15 20 25 30-5-10-15-20-25-30
+-Add a positi veAdd a negati ve
Negati ves make it opposite!
0 5 10 15 20 25 30-5-10-15-20-25-30
+-Subtract a posit ive
0 5 10 15 20 25 30-5-10-15-20-25-30
+-Subtract a negati veSubtract a positive
Negati ves make it opposite!
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Change the operation, AND change the sign!
(-4)
Whats the opposite,
of the opposite? THE SAME!
- (+4)+
(6)- (-6)+
(-3)+ (+3)-
(5)+ (-5)-
Now usethe
addition
rules!
D i l
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Decimals:Multiplication
When mult iplying decimals, we do not need to line up thedecimals like addit ion and subtraction.
Ignore the decimals at first, and multiply the numbers only.
After you have multiplied, count the number of decimals inthe original numbers.
The amount of decimals before and after multiplicationmust be the same!
13.7x 0.78
42.2x 12
320x $28.45
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44
4
Decimals: Division
Just like with fractions, it is not possible to divide bya decimal, so we must convert it first.
8 2 =80 20 =
800 200 4 =
x10
x100
8000 2000 =x1000
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Decimals: Division
To divide by a decimal , we need to multiply by afactor of 10 in order to remove the decimal.
We must also multiply the number being divided by
the same amount.
804 5.0 25.
x100
0
x100
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Multiplying and Dividing
Negative NumbersWhen multiplying and dividing negati ve numbers,first remember that mult iplication is repeated
addition!+(+2) + (+2) + (+2) + (+2) =
0 5 10 15 20 25 30-5-10-15-20-25-30
+-+8
+8
(+4) x(+2)= +8
Add a positive
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Multiplying and Dividing
Negative NumbersWhen multiplying and dividing negati ve numbers,first remember that mult iplication is repeated
addition!+(-2) + (-2) + (-2) + (-2) =
0 5 10 15 20 25 30-5-10-15-20-25-30
+--8
-8
(+4) x(-2) = -8
Add a positiveAdd a negati ve
Opposite
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Multiplying and Dividing
Negative NumbersWhen multiplying and dividing negati ve numbers,first remember that mult iplication is repeated
addition!
0 5 10 15 20 25 30-5-10-15-20-25-30
+-
-8-(+2) - (+2) - (+2) - (+2) =
(-4) x(+2)= -8
-8
Subtract a positive
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Multiplying and Dividing
Negative NumbersWhen multiplying and dividing negati ve numbers,first remember that mult iplication is repeated
addition!
0 5 10 15 20 25 30-5-10-15-20-25-30
+-+8
-(-2) - (-2) - (-2) - (-2) = +8(-4) x(-2)= +8
Subtract a negati veSubtract a positive
Opposite
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Multiplying and
Dividing NegativeTo multiply or divide with negative numbers,mult iply or divide like normal,
your sign will be based on the amount of negatives.
x + -
+ + --
- +
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hundredthstwentyfour
Decimals: ConvertingConverting from a decimal to a fraction is easy. . .
IF, you know your place values!
0.6 tenthssixsix tenths = 6
10
= 3
5
0.24 hundredthstwentyfour =24
100
= 6
25
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Converting from a fraction to a decimal is easy. . .IF, you remember fractions are division problems!
Decimals: Converting
6256
25
0.24
.00- 50
100- 1000
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hundredths
twentyfour
0.24hundredths
twentyfour
= 24
100
= 6
25
Decimals: ConvertingOccasionally we can use the reverse of our
decimal to fraction method,but only if we can make the denominator
a factor of 10.