Place Value
Hundred Ten
Hundred Ten
Millions Millions Millions Thousands Thousands Thousands Hundreds Tens Ones
4
7
3
1
2
2
8
1
0
Standard Form: 473,122,810
Expanded Form: 400,000,000 + 70,000,000 + 3,000,000 + 100,000 + 20,000 + 2,000 + 800 + 10 + 0
Expanded form using Powers of 10:
(4 x 108) + (7 x 107) + (3 x 106) + (1 x 105) + (2 x 104) + (8 x 102) + (1 x 101)
Word Form: Four hundred seventy-three million, one hundred twenty-two thousand, eight hundred ten.
Order from “Least” to “Greatest”:
5,293,078 ; 5,294,278 ; 5,293,288
Step 1: Start at the left. Compare the digits in the same position.
5,293,078
5,294,278
Least
5,293,288
Greatest
5,293,078 ; 5,293,288 ; 5,294,278
Estimation
Estimate sums, differences, products, and quotients of whole numbers. First you must use rounding!
Round to the nearest hundred
226
200
+186 +200
400
Round to the nearest ten
226
230
+186 +290
420
*When rounding, look at the digit to the right. If the digit 5-9 round up. If the digit is 0-4 it stays the
same.
24
x 36
20
x 40
800
29,437
-12,426
30,000
-10,000
20,000
21 42
2
20 40
Exponents
75
Exponent- tells you how many times the base number is multiplied by itself
Base- Is the number being multiplied by itself
Written as Factors:
7x7x7x7x7
Order of Operations
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction
(Multiplication and Division are completed by whichever comes first going left to right)
(Addition and Subtraction are completed by whichever comes first going left to right)
Example:
(2²+2³)² x (4-1)
(4+8)² x 3
12² x 3
144 x 3 = 432
Algebra Properties
1. Commutative Property – if the order of the addends or factors change, the sum or
product stays the same.
For example:
Addition:
4+3=7
Multiplication:
3+4=7
4 x 3 = 12
3 x 4 = 12
2. Associative Property – whatever way addends or factors are grouped does not change
the sum or the product
For example:
Addition:
(2 + 4) + 6 = 12
2 + (4 + 6) = 12
Multiplication:
(2 x 4) x 6 = 48
2 x (4 x 6) = 48
3. Distributive Property- Multiplying a sum by a number is the same as multiplying each
addend by the number and then adding the product.
For Example:
Over Addition:
8 x (5 + 3) = (8 x 5) + (8 x 3)
Over Subtraction:
8 x (5 - 3) = (8 x 5) - (8 x 3)
4. Identity Property
Of Addition- The sum of zero and any number is that number
4+0=4
1,276 + 0 = 1,276
Of Multiplication- The product of any number and one is that number
4x1=4
1,276 x 1 = 1,276
5. Zero Property of Multiplication – the product of any number and zero is zero
For example:
nx0=0
where (n) is any number