number sense: decimals

8/4/2019 Number Sense: Decimals

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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



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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



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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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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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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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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.

number sense: decimals

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