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Dividing by 10

Moving the decimal point to the left

Multiplying by 10

Moving the decimal point to the right

When you change the position of the decimal point in a coefficient value

you have to adjust the value of the exponent in order avoid changing the actual value.

decrease the value of the exponent by 1 (dividing by 10)

When moving the decimal point to the right (multiplying by 10)

When moving the decimal point to the left (dividing by 10)

increase the value of the exponent by 1 (multiplying by 10)

To multiply powers of 10:

Step 2. Add the exponents of the factors. The result is the exponent of the product. Of course the base of 10 remains unchanged.

To divide powers of 10:

Step 2. Subtract the exponents of the terms — numerator minus denominator. The result is the exponent of the quotient.

same exponent

Adding and subtracting powers of ten can be a bit more complicated than multiplying and dividing. The main problem is that powers of ten can be added or subtracted only when both terms have the

Are Equal

Powers of ten can be added or subtracted only when their exponents

When the exponents are not the same

rewrite one of the terms so that the exponents are equal

Engineering notation

is a special form of power-of-10 notation where the exponents for the 10s must be 0 or multiples of 3. There must be 1, 2, or 3 digits on the left side of the decimal point.

valid powers of 10 for engineering notation are:

10^3 10^6 10^9 10^ -3 10^ -6 10^ -9 10^0

Valid powers-of-10 for engineering notation

must be multiples of 3 or 0

decrease the power-of-10 exponent by the same number of units

When you move the decimal point in the coefficient to the right

increase the power-of-10 exponent by the same number of units

When you move the decimal point in the coefficient to the left

When you increase the value of the power-of-10 exponent

move the decimal point the same number of units to the left

When you decrease the value of the power-of-10 exponent

move the decimal point the same number of units to the right

Base

the number that is written with an exponent

Density Property

the property that states that between any two real numbers, there is always another real number

exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself

exponential form

a number is in this form when it is written with a base and an exponent

Hypotenuse

in a right triangle, the side opposite the right angle

Irrational Number

A number that cannot be written as a fraction with a numerator and a denominator that are integers. The decimal representation of a rational number either ends or repeats.

Legs

in a right triangle, the sides that include the right angle; in an isosceles triangle, the pair of congruent sides

monomial

a number or a product of numbers and variables with exponents that are whole numbers

Perfect Square

the number that forms when two same numbers are multiplied together

power

a number produced by raising a base to an exponent

Principal Square Root

the nonnegative square root of a number

Pythagorean Theorem

in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs

real number

combonation of rational and irrational numbers

Scientific notation

where a number is written into 2 parts first just the digits (with decimal point after first digit) followed by ×10 to a power

Square Root

when multiplying a number by itself to get a square number

13²

169

14²

196

15²

225

16²

256

17²

289

18²

324

19²

361

20²

400

21²

441

22²

484

23²

529

24²

576

25²

625

26²

676

27²

729

28²

784

29²

841

30²

900

Exponent or power tells you...

how many bases to multiply together

b¹

Any base to the first power is just that base.

3¹ = 3

What are 3¹ through 3⁴...

5¹ = 5

What are 5¹ through 5³...

4¹ = 4

What are 4¹ through 4³...

Calculate -3² and (-3)²

-3² = -(3²) = -9

Positive

Counting from the decimal point to the right makes the exponent ___________________________________________

Negative

Counting from the decimal point to the left makes the exponent ___________________________________

Solve for x² = 16

* an even exponent can hide the sign of the base! x = 4 or x = -4

a⁵ × a³ =

a⁵ × a³ = a⁸

y(y⁶) =

y(y⁶) = y¹ × y⁶ = y⁷

2³ × 2ⁿ

2³ × 2ⁿ = 2³⁺ⁿ

a¹⁵/a¹³ =

a¹⁵/a¹³ = a¹⁵⁻¹³ = a²

a⁰ =

a⁰ = 1

a³ / a⁵ =

a³ / a⁵ = a³⁻⁵ = a⁻² OR 1/a²

x²x³

x²⁺³ or x⁵

x²+x²

2x²

x⁵/x³

x⁵⁻³ or x²

x²y²

(xy)²

x³/y³

(x/y)³

(x/y)⁵

x⁵/y⁵

(x³)²

x³*² or x⁶

x³⁻⁷

x³/x⁷ or x⁻⁴ or 1/x⁴

√x²

x

√(a²+a²)

√(2a²)

5√x

3√x + 2√x

√(36*16)

√36 * √16 or 6*4

√(25/4)

√25 / √4 or 5/2

√(a²b)

√a² * √b or a√b

Simplify: 1/√3

(1/√3) * (√3/√3) = (√3/3)

x⁰

1

x⁻²

1/x²

x¹

x

x^½

√x

x^¾

⁴√x³

8^²/³

³√8² = ³√64 = 4

Πr²

Area of circle

Circumference

2πr

Sector ratio

(∠/360°) = (Area of sector/ Area of circle)

Arc ratio

(∠/360°) = (Arc Length/ Circumference)

360°

Degrees in a circle

180°

Degrees in a line

slope

(y₂-y₁)/(x₂-x₁)

y=mx+b

Line equation

Positive slope

Moves up

Negative slop

Moves down

horizontal line

Slope of zero

undefined slope

Vertical line

½bh

Area of Triangle

Triangle height

Perpendicular to base. Does not have to be measured in the triangle. Every triangle has 3 heights and 3 bases.

Triangle sides rule

Equal sides are across from equal angles. Largest side is across from the largest angle

isosceles triangle

Triangle with 2 equal sides and 2 equal angles.

equilateral triangle

Triangle with a 90° angle

Third side rule

The third side of any triangle must be between the sum and difference of the other two sides.

Triangle in a semi-circle

A triangle inscribed in a semicircle is a right triangle.

1:1:√2

Side Ratio: 45-45-90 Triangle

Side Ratio: 30-60-90 Triangle

1:2:√3 (2 is hypotenuse)