In this topic, students will:
locate repeating decimals on a number line
write repeating decimals as fractions
classify a number as rational or irrational
understand the concepts of square roots and perfect squares
approximate square roots by using perfect squares
compare and order rational and irrational numbers
evaluate square roots and cube roots to solve problems
evaluate perfect squares and perfect cubes
solve equations involving perfect squares or cubes
solve equations involving imperfect squares or cubes
multiply and divide expressions and integer exponents
find the power of a power
simplify exponential expressions using the Zero Exponent Property and the Negative Exponent Property
estimate and compare very large and very small quantities using powers of 10
write very large and very small numbers in scientific notation
convert scientific notation to standard form
add, subtract, multiply, and divide numbers in scientific notation
Vocabulary:
Irrational numbers - any quantity or term that cannot be represented as a simple fraction
Perfect square - the product of a rational number multiplied by itself
Square root - the square root of a number is a term that, when multiplied by itself, gives the number
Cube root - the cube root of a number is a term that, when multiplied by itself three times, gives the number
Perfect cube - the product of a rational number multiplied by itself three times.Â
Power of powers property - when you have an exponent raised to a power, keep the base and multiply the exponents
Product of powers property - to multiply two powers with the same base, keep the common base, and add the exponents
Powers of Products property - to multiply two powers with the same exponent and different bases, multiply the bases, and keep the exponent
Quotient of powers property - when dividing two powers with the same base, we subtract the exponents
Negative exponent property - any nonzero number raised to a negative power is equal to its multiplicative reciprocal
Zero exponent property - any nonzero number raised to the power of zero is equal to 1
Scientific notation - the purpose is to write large terms using less numbers. This is represented by a decimal term between one and ten that is multiplied by ten.