Place Value

1
Place Value

• The place value tells you how much that digit
  represents.

• Standard form 48,362,078,510,009
• Word form forty-eight trillion, three hundred
  sixty-two billion, seventy-eight million, five
  hundred ten thousand, nine
• Number Word form 48 trillion, 362 billion, 78
  million, 510 thousand, 9

2
Rounding

• Adjusting a number to make it more convenient to
  use, according to a given place value.
• Example 2,571 rounded to the nearest hundred is
  2,600

3
base

• The number to be multiplied

exponent or power

• The number that tells you how many times the base
  is used as a factor.

factor

• When you multiply numbers, each number is called
  a factor.

product

• The answer to a multiplication problem

4

• Exponential notation 27
• Expanded form 2x2x2x2x2x2x2 27
• Standard notation 128
• 52 is 5x5 or 5 squared.
• 83 is 8x8x8 or 8 cubed.

5

• Compatible numbers-pairs of numbers that can be
  computed easily. Ex. 251875, combine 2575100,
  10018118
• Compensation-choosing a number close to the
  number in the problem, then adjusting the answer
  to compensate for the number you chose Ex. 583
  try 603180 and then subtract 23 180-6174

6
Properties

• 1. Distributive Property- break numbers into
  smaller numbers, calculate, then put your answers
  together Ex. 32x5 (302)x5 or
• (30x5) (2x5) 15010160
• The 5 gets distributed to the other numbers.

7
Properties

• Commutative- changing order of addends or factors
  does not change the sum or product.
• Example 4x728 and 7x428
• Associative- changing the grouping of addends or
  factors does not change the sum or product.
• Example (53)715 and 5(37)15

8
Properties

• Zero Property of addition - if you add zero to
  any number the sum will be that same number. Ex.
  303
• Identity property of multiplication if you
  multiply any number by one the product will be
  that same number. Ex. 3x13
• Zero property of multiplication if you multiply
  any number by zero, the product is zero. Ex.
  3x00

9
Order of Operations

• Please
• Excuse
• My Dear
• Aunt Sally

• Parentheses
• Exponents
• Multiplication Division
• (left to right)
• Addition Subtraction
• (left to right)

10
variable

• A quantity that can change or vary, often
  represented with a letter a3? a is
  the variable

constant

• A quantity that does not change a3? 3 is
  the constant

expression

• A mathematical phrase involving constants,
  variables, and operation symbols.

11
Vocabulary

• Sum The answer to an addition problem.
• Difference The answer to a subtraction problem
• Product the answer to a multiplication problem
• Quotient the answer to a division problem

12
equation

• A mathematical sentence that uses an equal sign,
  , to show that two expressions are equal.

13
Scientific Notation

• A number in scientific notation is written as the
  product of a decimal number and a power of 10.