Unit 2

Quotient of a power rule

When you are dividing like terms with exponents, use the Quotient of Powers Rule to simplify the problem. This rule states that when you are dividing terms that have the same base, just subtract their exponents to find your answer. The key is to only subtract those exponents whose bases are the same.

Terminating decimal

A decimal number that has digits that do not go on forever. Examples: 0.25 (it has two decimal digits) 3.0375 (it has four decimal digits) In contrast a Recurring Decimal has digits that go on forever Example: 1/3 = 0.333... (the 3 repeats forever) is a Recurring Decimal, not a Terminating Decimal

Repeating decimal

A decimal number that has digits that repeat forever. Examples: 1/3 = 0.333... (the 3 repeats forever) 1/7 = 0.142857142857... ( the "142857" repeats forever) 77/600 = 0.128333... (the 3 repeats forever) The part that repeats is usually shown by placing dots over the first and last digits of the repeating pattern, or sometimes a line over the pattern. Also called a "Repeating Decimal".

Negative exponent rule

A negative exponent means how many times to divide by the number. Example: 8-1 = 1 ÷ 8 = 1/8 = 0.125. Or many divides: Example: 5-3 = 1 ÷ 5 ÷ 5 ÷ 5 = 0.008.

Perfect square

A number made by squaring a whole number. 16 is a perfect square because 42 = 16 25 is also a perfect square because 52 = 25 etc

Rational number

A number that can be made by dividing two integers. (Note: integers have no fractions.) The word comes from "ratio". Examples: • 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2) • 0.75 is a rational number (3/4) • 1 is a rational number (1/1) • 2 is a rational number (2/1) • 2.12 is a rational number (212/100) • −6.6 is a rational number (−66/10) But Pi is not a rational number, it is an "Irrational Number".

Integer

A number with no fractional part. Includes: • the counting numbers {1, 2, 3, ...}, • zero {0}, • and the negative of the counting numbers {-1, -2, -3, ...} We can write them all down like this: {..., -3, -2, -1, 0, 1, 2, 3, ...} Examples of integers: -16, -3, 0, 1, 198

Irrational number

A real number that can NOT be made by dividing two integers. (Note: integers have no fractions.) The decimal goes on forever without repeating. Example: Pi is an irrational number.

Radical

An expression that has a square root, cube root, etc.

Power of a power rule

- The Power of a Power Rule states (bm)n is equal to bmn. This rule means that you multiply the exponents together and keep the base unchanged.

Base

Definition 1: The number that is going to be raised to a power. Example: in 82, 8 is the base Definition 2: How many numbers used in a number system The decimal number system that we use every day has 10 digits {0,1,2,3,4,5,6,7,8,9} and so it is Base-10. Binary digits can only be 0 or 1, so they are Base-2.

Expanded form

Expanded Form is a way to write numbers by adding the value of its digits. Example: 1,000 + 900 + 50 + 4 = 1,954. Example 1: Write and Read the number 6,174. Standard Form. Word Name.

Scientific notation

Scientific notation is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits.

Standard form

Standard form is a way of writing down very large or very small numbers easily. Sign up to practice Algebra.

Non-terminating

The bar notation indicates that an infinite number of repeating 3's are required to represent this fraction. = 3.1415926... is another example of a number with a nonterminating decimal expansion. The ellipsis indicates that there are an infinite number of non-repeating digits following the decimal point.

Perfect cube

The cube root of a number is ... ... a special value that when cubed gives the original number. The cube root of 27 is ... ... 3, because when 3 is cubed you get 27.

Cube root

The cube root of a number is a special value that, when used in a multiplication three times, gives that number. Example: 3 × 3 × 3 = 27, so the cube root of 27 is 3.

Product of a power rule

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.

Exponent

The exponent of a number says how many times to use that number in a multiplication. It is written as a small number to the right and above the base number. In this example: 82 = 8 × 8 = 64 (The exponent "2" says to use the 8 two times in a multiplication.) Other names for exponent are index or power.

Whole number

The numbers {0, 1, 2, 3, ...} etc. There is no fractional or decimal part. And no negatives. Example: 5, 49 and 980 are all whole numbers. Whole Number

Square root

The square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)

Natural number

The whole numbers from 1 upwards: 1, 2, 3, and so on ... Or from 0 upwards in some fields of mathematics: 0, 1, 2, 3 and so on ... No negative numbers and no fractions.

Zero rule

The zero exponent rule is one of the rules that will help you simplify exponents. Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent, or power.