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z. Math > Week 1 > Flashcards

Week 1 Flashcards

1
Q

percentage -> fraction

A

/100

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2
Q

fraction -> percentage

A

*100

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3
Q

decimal -> percentage

A

*100

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4
Q

fraction -> decimal

A

N/D

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5
Q

decimal -> fraction

A

decimal (a.bc…) = a bc/100

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6
Q

Natural Numbers (N)?

A

(also called positive integers, counting numbers, or natural numbers); They are the numbers {1, 2, 3, 4, 5, …}

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7
Q

Whole Numbers (W).

A

This is the set of natural numbers, plus zero, i.e., {0, 1, 2, 3, 4, 5, …}.

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8
Q

Integers (Z).

A

This is the set of all whole numbers plus all the negatives (or opposites) of the natural numbers, i.e., {… , ⁻2, ⁻1, 0, 1, 2, …}

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9
Q

Rational numbers (Q).

A

This is all the fractions where the top and bottom numbers are integers; e.g., 1/2, 3/4, 7/2, ⁻4/3, 4/1 [Note: The denominator cannot be 0, but the numerator can be].

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10
Q

Real numbers (R),

A

(also called measuring numbers or measurement numbers). This includes all numbers that can be written as a decimal. This includes fractions written in decimal form e.g., 0.5, 0.75 2.35, ⁻0.073, 0.3333, or 2.142857. It also includes all the irrational numbers such as π, √2 etc. Every real number corresponds to a point on the number line.

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11
Q

Discrete and continuous numbers?

A

Discrete:

Natural, Whole, Integers, Rationals

This means that they are separate and distinct entities. In fact each of these sets is countable.

Continuous:

Real numbers cannot be counted. This is because they are continuous. Between any two real numbers, however close they may be, there are infinitely more real numbers.

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12
Q

e

A

e=(1 + 1/n)^n

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13
Q

3/6i

A

i is in the Den

Rationalize the Denominator

= 3*i/6i*i

= 3i/-6

= i/-2 OR - i/2 OR - 1/2 i

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14
Q

Index Laws?

Mult

Div

Powpow

Fractional

A

an * am = an+m

an / am = an-m

(an)p = an*p

ax/y = y√ax

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15
Q

Index Laws?

Negative

Zero

Advanced (4)

A

a-n = 1/an

a0 = 1

ap/q = q√ap = (a1/q)p

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16
Q

25^1/2

A

√25 = 5

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17
Q

-2^4

expand

A

-(2*2*2*2) = -16

NOT

(−2)*(−2)*(−2)*(−2) = 16

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18
Q

4 - 3 1/8

??? fix

A

7/8

OR

0.78

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19
Q

5127 * 4265

A

align

5127

4265

25635

(5 * all)

5127

4265

25635

(6 * all) (add 0)

307620

5127

4265

25635

307620

(2 * all) (add 00)

1025400

ETC…

THEN ADD ALL PRODUCTS:

5127

4265

_____

25635

307620

1025400

20508000

_________

21866655

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20
Q

Long Division?

A

Dividend / Divisor = Quotient

Quotient

Divisor (Dividend

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21
Q

8764 / 4

A
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22
Q

10π/5

A

2π

10π/5π = 2

23
Q

the number e can be calculated by adding and infinite number of terms of:

A

1 + 1/1 + 1/1*2 + 1/1*2*3 + 1/1*2*3*4 …

add each of the first 6 terms as decimals to 5 decimal plaveces. Add these 6 terms to get an approximate value of e

24
Q

4√20 - 2√5

A

Q: 4√20 - 2√5

= 4 * √4 * √5 - 2√5

= 4 * 2 * √5 - 2√5

= 8√5 - 2√5

= 6√5

25
Q

2√10 × 3√5

A

= 6√50

= 6 × √25 × √2

= 6 × 5 × √2

= 30√2

26
Q

5−2√2 +√9

A

= 5−2√2 + 3

= 8−2√2

27
Q

6√5 + 4√5×2√5

A

Q: 6√5 + 4√5×2√5

= 6√5 + 8×√25

= 6√5 + 8×5

= 6√5 + 40

28
Q

−3√8×−4√6

A

Q: −3√8×−4√6

= 12√48

= 12×√16×√3

= 12×4×√3

= 48√3

29
Q

18√18/256

A

Q: 18√18/256

= 9√18/128

= 9*√9*√2/128

= 9*3*√2/128

= 27√2/128

30
Q

√5*6√2*2√2/5√8*2√5

A

Q: √5*6√2*2√2/5√8*2√5

= 6√2*2√2/5√8*2

= 12√4/5√4√2*2

= 12*2/5*2√2*2

= 24/20√2

= 12/10√2

= 6/5√2

31
Q

6/5√2

rationalize the denominator

A

Q: 6/5√2

= 6/5√2 * √2/√2

= 6√2/5√4

= 6√2/5*2

= 6√2/10

= 3√2/5

32
Q

i

A

= √-1

33
Q

i^0

A

1

34
Q

i^2

A

-1

35
Q

i^3

A

-i

(i^2 * i) = -i

36
Q

i^4

A

1

(i^2 * i^2) = -1 * -1 = 1

37
Q

3i * 2i^3

A

= 6i^4

(i^4 = 1)

= 6

38
Q

√-49

A

= √49 * √-1

= 7i

39
Q

4/5i

A

Q: 4/5i

= 4*i/5i*i

= 4i/5i^2

= 4i/-5

= - 4i/5

40
Q

2i^7

A

= -2i

41
Q

14a^2b-5a^2b+a^2

A

9a^2b+a^2

this cant be simplified further as 9a^2b and a^2 are unlike terms

42
Q

20h^2k^3 / 5hk/2

A

20h^2k^3 / 5hk/2

= 20h^2k^3/1 * 2/5hk

= 8hk^2/1

= 8hk^2

43
Q

3c^−3d^2*(c^2d)^−3

A

Q: 3c^−3d^2*(c^2d)^−3

= 3d^2/c^3 * c^-6d^-3

= 3d^2/c^3 * 1/c^6d^3

= 3/c^9d

44
Q

25^-3/2

A

Q: 25^-3/2

= 1/25^3/2

= 1/(25^1/2)^3

= 1/5^3

= 1/125

45
Q

149300000

Write in Scientific Notation

A

149300000

=

1.493*10^8

46
Q

0.00000462

Write in Scientific Notation

A

0.00000462

=

4.62×10^−6

47
Q

0.0030028

Write in Scientific Notation

A

0.0030028

=

3.0028×10^−3

48
Q

8.13×10^−5

Write in Standard Form

A

8.13×10^−5

=

0.0000813

49
Q

1.037×10^8

Write in Standard Form

A

1.037×10^8

=

103700000

50
Q

6.458×10^−3

Write in Standard Form

A

6.458×10^−3

=

0.006458

51
Q

5.080

sig figs?

A

has four significant figures

52
Q

1060

sig figs

A

has three significant figures

53
Q

1.0

sig figs?

A

has two significant figures

54
Q

0.0041

sig figs?

A

has two significant figures

z. Math (14 decks)

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