The document provides instructions and examples for various math concepts: 1) It explains how to round numbers to a given place value or significant figure, and provides examples of rounding 89,475 to the hundredth place and to one significant figure. 2) It demonstrates how to translate English phrases into math equations, such as "Max scored 2 times more goals than bob" becoming M=2B. 3) It defines index notations, square numbers, cube numbers, and provides examples of each.

1. Math Journal
Chapters 1 and 3
BY : ERNESTO TOVAR

2. Describe how to round a number to a given place
value or significant figure.
When Rounding a number you always have to check the
number on the right. If it’s lower than 5 then you can’t
round it and all the other numbers on the right become
0. If it’s greater than 5 then you can round it to the
next significant figure.

3. Rounding Examples
 Round 89,475 to the hundredth place.
The hundredth place is 4 and the tenth’s place, 7, which is greater than
5, therefore you can round 4 to the next value which is 5.The result is
89,500
 If you want to round to one significant figure then
you go backwards 89,475, so the 8 will be the
significant figure and when you round it it becomes 9
so it will be 90,000
 If you want to round to two significant figures it will
be the 9 round it and it will be 89,000

4. Translating English to Math
When translating English into Math, firstly you must
know the math to English dictionary. For example
Max scored 2 times more goals than bob, It will be
M=2B,also we don’t 2xB because in algebra when
you write 2B you know it’s 2xb.
Example 2. John has 4 more apples than Carlos=
J=4tC
Example 3. Alex has 3 apples less than Ralph= R= A-3
Example 4. Jackie and Bruce scored 3 times less goals
than Justin and Jason= J+B= U+N/3

5. Index Notations
Index notations are a different way to express numbers
as a result of multiplication.
Example 1. 3x3x3=27
Example 2.6x6x4=36x4=144
Example 3.7x7x7x2=343x2=686

6. Square Number
A square number is a number by the power of 2. We
don’t say by the power of two we usually say 2
squared. We call it a square number because square
numbers are like finding the area of a square.
Example 1: 2=22 = 4
Example 2: 3=32 = 9
Example 3: 4=42 = 16

7. Cube Numbers
A cube number is the same thing as a square, but
instead of power of 2 is power of 3 and we write it
like this 43. We call it a cube number because cube
numbers are like finding the volume of a cube.
Example 1: 4=43 = 64
Example 2: 5=53 = 125
Example 3: 6=63 =216

8. Order of Operations
The order of operations is how math problems can be
organized so you get the right answer. It is really
important if they give you a problem like this: 50(10+15)-
30 you’ll be able to figure it out. If we didn’t have the
order of operations everyone would get a different
answer
Step 1. Parenthesis
Step 2. Exponents
Step 3. Division
Step 4. Multiplication
Step 5. Addition and Substraction
Remember always start from left to right

9. Order of Operations Examples
 Example 1. 65+(10-5)-9=61, Always do parenthesis
first .
 Example 2. 49(8/64)+23=424, In algebra when the
number is next to the math problem you don’t add
you multiply.
 Example 3. 37+(4/8x10)100= 570, Always remember
the order of operations and always go from left to
right or you will get it wrong.

10. Factors
The numbers that are being multiplied in a
multiplication are called the factors of the final
number.
Example 1. The factors of 12 are 1,2,3,4,6,12
Example 2. Factors of 6: 1,2,3,6
Example 3: Factors of 14: 1,2,7,14

11. Intergers
Intergers are all the numbers below and above zero, or
all the negative and positive numbers. Intergers are
important because they are used in today’s world for
calculations, equations etc.
Example 1. -5
Example 2. 28
Example 3. -1200

12. Adding and Subtracting Intergers
Adding and subtracting intergers is pretty easy if you know
the key rules. When it’s -3+7 it will be 4,but when it’s
double negative like this: -5+-14, you add, so it will be -
19. If it’s a double negative with brackets -3-(-4) you also
add
Example 1.-14-(-13)=-1
Example 2. -25+-16=-41
Example 3. -14+15=1
Key Rules Addition: If signs are the same add up the
numbers and keep the sign.
Key Rules Subtraction: Add the opposite.

13. Multiplying and Dividing Intergers
Multiplying and dividing intergers is the same thing as
adding subtracting except that you have multiply and
divide and you have to know the key rules.
Key Rules: If there are two different signs the answer
has to be a negative number. If the signs are the
same it has to be a positive number.
Example 1. -8x7=-56
Example 2. -10x-10= 100
Example3. -4/20=-5

14. Square Roots
Square roots is the opposite of square numbers. Before
doing square roots you must first know the perfect
squares and key rules. For example square root of 16
is 4 square root of 64 is 8.
Key Rules: “what number times itself = x”?
Example 1. Square root of 9 is 3
Example 2. Square root of 49 is 7
Example 3. Square root of 6 is approximate to 2.5

15. Cube Roots
Cube roots are the same thing as square roots except
it’s the opposite of cube numbers. Before doing cube
roots you also need to remember your perfect cubes
and squares and key rules.
Key Rules: “What number times itself 3 times = x”?
Example 1. Cube root of 27 is 3
Example 2. Cube root of 8 is 2
Example 3. Cube root of 6 is approximate to 1.8

16. How do we Find Higher Power Roots of
Numbers?
Finding power roots of higher numbers is the same thing as
cube roots and square roots except it’s a higher number than
3. For example fourth roots, are: “ a number times itself 4
times = x”. Same with fifth roots, sixth roots and so on.
Example 1. Fifth root of 3125 is 5, 5 times itself 5 times equals
3125
Example 2. Fourth root of 16 is 2, because 2 times itself 4 times
equals 16
Example 3. Sixth root of 24 is 1.69838133, when a number like
this shows up on your calculator just round it off to one or two
decimal places and you will get an approximate value of the
sixth root of 24. It will be 1.7, 1.7 times itself 6 times = 24