Mathematics: Measurement and Functions

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Questions and Answers

What is the definition of accuracy?

The possible y values or output

A description of how close a measurement is to the true value of the quantity measured (correct)

Exactness of a measurement

The exact number of significant figures in a measurement

What does precision refer to?

The amount of significant figures in a number

The relationship between input and output values

The exactness of a measurement (correct)

The set of possible x values

What are significant figures?

The amount of significant figures in a number that can be found by counting.

What is a relation in mathematics?

Describes a relationship and pairs input values with output values. Signup and view all the answers

What defines a function?

None of the same input values, special relationship in that each input value is paired with only one output value. Signup and view all the answers

What does range refer to?

Possible y values or the output. Signup and view all the answers

What does domain refer to?

Possible x values or the input. Signup and view all the answers

Any number (except 0) with an exponent of 0 equals ______.

1 Signup and view all the answers

What is the Negative Exponent Property?

Any number raised to a negative power is equivalent to the reciprocal of the positive exponent of the number. Signup and view all the answers

What is the Product of Powers Property?

To multiply two powers with the same base, add the exponents. Signup and view all the answers

What is the Quotient of Powers Property?

To divide two powers with the same base, subtract the exponents. Signup and view all the answers

What is the Power of a Product Property?

To find a power of a product, find the power of each factor and then multiply. Signup and view all the answers

What is the Power of a Quotient Property?

To find a power of a quotient, find the power of each part of the quotient, and then divide by canceling common factors. Signup and view all the answers

What is the Power of a Power Property?

To find a power of a power, multiply the exponents. Signup and view all the answers

What are rational exponents?

Exponent expressed as a fraction, which can be converted to radical expressions. Signup and view all the answers

What are unequal bases?

When working with unequal bases, it may be necessary to rewrite them with common bases. Signup and view all the answers

What are real numbers?

A number that is rational or irrational; this includes all non-imaginary numbers. Signup and view all the answers

What are irrational numbers?

A number that cannot be expressed as a ratio of two numbers (fraction), including decimals that never stop. Signup and view all the answers

What are rational numbers?

A number that can be expressed as a ratio of two numbers (fraction), including decimals that terminate or repeat. Signup and view all the answers

What are integers?

Positive and negative whole numbers including zeros. Signup and view all the answers

What are whole numbers?

All positive whole numbers including zero. Signup and view all the answers

What are natural numbers?

All positive whole numbers, not including zero. Signup and view all the answers

What does PEMDAS stand for?

Parentheses, Exponents, Multiplication and Division (reversible), Addition and Subtraction (reversible). Signup and view all the answers

What are coefficients?

The numbers that come before the variable telling you how many times the variable has been added. Signup and view all the answers

What are factors?

Values you can multiply together. Signup and view all the answers

Study Notes

Measurement Terminology

Accuracy refers to how close a measurement is to the true value of a quantity.
Precision indicates the exactness of a measurement.
Significant Figures are the digits in a number that contribute to its precision, determined by counting.

Mathematical Relationships

Relation describes associations between input (x) and output (y) values.
Function specifies a special type of relation where each input value corresponds to only one output value.

Key Concepts in Functions

Domain represents all possible input (x) values.
Range consists of all possible output (y) values.

Exponent Properties

Zero Exponent Property states that any non-zero number raised to the power of zero equals one.
Negative Exponent Property indicates that any number raised to a negative power is equivalent to the reciprocal of the number raised to the positive exponent.
Product of Powers Property requires adding exponents when multiplying two powers with the same base.
Quotient of Powers Property involves subtracting exponents when dividing powers with the same base.
Power of a Product Property entails finding the power of each factor in a product and multiplying the results.
Power of a Quotient Property requires applying the power to both the numerator and denominator, canceling any common factors.
Power of a Power Property involves multiplying the exponents when raising a power to another power.
Rational Exponent Property shows that fractional powers can be converted to radical expressions, where the numerator is the exponent and the denominator is the index of the radical.

Types of Numbers

Real Numbers include all rational and irrational numbers; they encompass every non-imaginary number.
Irrational Numbers cannot be expressed as a simple fraction, featuring non-repeating, non-terminating decimals.
Rational Numbers are represented as fractions, including terminating or repeating decimals.
Integers encompass positive and negative whole numbers, including zero, excluding fractions and decimals.
Whole Numbers include all positive integers as well as zero but exclude negative values.
Natural Numbers consist solely of positive integers, excluding zero.

Order of Operations

PEMDAS is a mnemonic for the order of operations:
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)

Algebraic Components

Coefficients are the numbers that precede variables, indicating how many times the variable is included in the expression.
Factors are values that can be multiplied together to yield a product.

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Description

This quiz tests your understanding of key concepts in measurement terminology and mathematical functions. Topics include accuracy, precision, significant figures, relations, functions, domain, range, and exponent properties. Sharpen your math skills and grasp these essential concepts.