unit conversion

the world’s most amazing number!

1) multiplication
2) division

3/3 = π/π = -4/-4 = 1

12 eggs = 1 carton
12 eggs / 1 carton = 1

conversion factor: a number that relates amount of one thing to amount of another.

cartons -> eggs 12eggs = 1carton
yards -> feet 3feet = 1yard
liters -> ounces
dollar -> Euros

1 mile = 5280 feet
1 gallon = 4 quarts
1 gram = 1000 milligrams
1 pound = 16 ounces

1 mile = 1.609 Km
if you run 5 km, 3.1 miles you run

1 mile = 1760 yards
1 yard = 3 feet
1 m = 1.093 yards
1 km = 1000m
1 m = 100cm
1m = 1000mm
1gal = 16cups
1 gal = 3.785liters

Ratios

Rates: compare two quantities with different units
Ratios: compare two quantities with the same units

ex. “three out of five dentists recommend toothtaste.”

1/2 exact same meaning 1:2

3/5 -> 3:5
8/10 -> 4:5
200/500 -> 2:5
2/9 -> 2:9

Rates

learning the ratio and rates is super important

35 MPH(unit)
-> 35 miles per hour

35 miles / 1 hour

example
$12 / 1hour, 4,000,000babies/1year, 260calories/20 ounces of coke

150 miles / 3 hours = 50 miles / 1 hour -> unit rate
50 miles per hour

A unit rate is any rate where the value of the denominator is 1

pretzelicious: $3.50, 15ounces -> $0.23/ounce
pretztastic: $3.6, 18ounce -> 0.20/ounce

Scientific Notation

US National Deficit: 17 trillion dollars
$17,000,000,000
1.7 * 10^10

10^4 = 10,000

15,000:standard notation
1.5 * 10^4:scientific notation

negative powers
1.5 * 10^-4 = 0.00015
3.2* 10^-5 = 0.000032

2,700,000,000 -> 2.7 * 10^9

convert to scientific notation
34,000,000 -> 3.4 * 10^7

Fraction

what is a fraction?
fraction = part / whole

mixed number has whole number and fractions
1+5/8

common denominators!
8/8 – 3/8 = 5/8 keep denominator same

circumference 88, 28.25
diameter 28, 9
circumference/diameter 3.14, 3.14
π = 3.14

radius * 2 = diameter
c = π*d
d = 3, c = 9.42
Area = πr^2

Intro to Exponents

3^2 = 9, base is three exponent
Exponents are powerful!

first power
3^1 = 3

dividing by the base
3^4
3^3
3^2 = 9
3^1 = 3
3^0 = 1
-1 * 4^2 = -4^2 = -16
(-4)^2 = 16

PEMDAS
parentheses, exponents, multiply, divide, add, subtract

more order of operations
6 / [4- (6-8)]+(-2)^3= -7

area of a square
l*l
l^2

Algebra Integers

Number Lines
– arrows on each end, zero, marks to indicate scale, positive negative direction

arrow, the lines extend on forever
infinity: goes on forever without limit
+ or –
infinity is the largest on positive

the truth about number line

absolute value: distance from zero, cannot be negative, |number|
sum: the result of adding number together
quatient: the result of division
associative property: +, *

function practice

func firstCharacter(of word: String) -> Character {
	return word[word.startIndex]
}

firstCharacter(of: "Mom")

import Fundation

func placeFirstLetterLast(myString: String){
	
}

func placeFirstLetterLast (myString: String) -> String {
	var myString = myString
	myString.append(firstCharacter(of: myString))
	return myString
}
func shortNameFromName(name: String) -> String {
	let lowercaseName = name.lowercaseString
	let vowelSet = CharacterSet(charactersIn: "aeiou")
}

shortNameFromName(name: "Nate")
//
shortNameFromName(name: "Talia")
//

func lyricsForName(lyricsTemplate: String, fullName: String) -> String {
	let shortName = shortNameForName(name: fullName)

	let lyrics = lyricsTemplate
		.replacingOccurrences(of: "<FULL_NAME>", with: fullName)
		.replacingOccurrences(of: "<SHORT_NAME>", with: shortName)

	return lyrics
}