Lesson 7: Prefixes and Power of 10 Flashcards
The expression 2x2x2 can be written using a _______ and an ________
Base
Exponent
2x2x2= 2^3, this is called a ________. The expression is read _________
Power
2 to the third power
An exponent may be _________, _________, or _________
positive
negative
Zero
A positive exponent indicates
how many times the base is used as a factor
A negative exponent indicates
how many times the reciprocal of the base is to be used as a factor
A zero exponent with a non zero base indicates
that the value of the power is 1
The expression 0^0 is ________
Undefined
To evaluate an expression that has a negative exponent, you must?
replace the base with it’s reciprocal and replace the exponent with its opposite
Any nonzero base to the power of 0 is
1
To multiply powers that have the same base
add the exponents and use the same base
Product of Powers states
For any number (a) except (a)=0, and all numbers (m) and (n): a^m x a^n = a^m+n
When an exponent is not written, it is
1
To divide the powers that have the same base
subtract the exponents and use the same base. Always subtract the exponent in the denominator from the exponent in the numerator
Quotient of Powers states
For any number “a” except “a”=0, and all number “m” and “n”: a^m/a^n = a ^m-n
Power of a Quotient states
For any nonzero numbers “a” and “b”, and all numbers “n”:
a/b)^n = (a^n/b^n
To simplify a power of a power
multiply the exponents and use the same base
Power of a Power states
For any nonzero number “a”, and all numbers “m” and “n”
a^m)^n=a^(m)(n
Scientific notation is used for
representing very large or very small quantities.
A number in scientific notation is a product of
(a number that is at least 1 and less than 10) X (a power of 10)
To write a number in scientific notation you must
- First move the decimal point to the immediate right of the first nonzero digit.
- Count the number of space you moved the decimal point
- Use that number as the exponent of 10
- If you moved the decimal point to the Left it is a positive exponent, If it was moved to the Right it is a negative exponent
The powers must have the same _______ to apply the Product of Powers and Quotient of Powers
base
Engineering notation is similar to scientific notation but,
requires the exponent in the power of 10 be divisible by 3
the multiplier in front of the power of 10 must be at least 1 but less than 1,000
What are the Powers of 10 in Engineering Notation?
Tera T 10^12 Giga G 10^9 Mega M 10^6 Kilo k 10^3 milli m 10^-3 micro u 10^-6 nano n 10^-9 pico p 10^-12
The Square of a number is the _________ of that number.
Second Power
A ______ of a number is a number that can be squared to get the given number.
Square root
Every positive number has a ________ square root and a _______square root
Positve
Negative
The Positive square root of a number is called the ________ and is the square root normally concerned with.
Principal square root
The Product Property of Square Roots states
For any numbers “a” and “b” where “a” greater than or equal to 0 and “b” greater than or equal to 0, the square root of the product of (a)(b) = the square root of “a” x the square root of “b”
Fraction Exponents, the square root of a number can be expressed using the fraction ____ as the exponent.
1/2
When converting from a prefixed number to a whole number you must
multiply by the power of 10 for that prefix
When converting from a whole number to a prefixed number you must
divide by the power of 10 or the value of the prefix
When converting from a prefixed number to another prefixed number you must
Convert from Prefixed number to Whole number (multiply by power of 10)
Whole number to new prefixed number (divide by power of 10)
