Rational vs Irrational Numbers
Is 0.75 rational or irrational?
Rational — it is a terminating decimal. It can be made a fraction
Why can a repeating decimal be written as a fraction?
Because a repeating decimal is a rational number, and rational numbers can be written as a fraction of two integers
Evaluate the square root of 49
7 and -7
Simplify. x^3 * x^4
x^7
What is 5^0?
1
Is 0.121212... rational or irrational?
Rational — it is a repeating decimal, and it can be written as a fraction.
Write 0.66666... as a fraction. Show your work using the equations
6/9
Evaluate the cube root of 27
3
x^12
Is the square root of 8 rational or irrational?
Irrational — 8 is not a perfect square.
Is 0.283746294... rational or irrational?
Irrational — it does not terminate or repeat.
Write 0.12121212... as a fraction. Show your work using equations.
12/99
Yes. 6 x 6 = 36
Simplify. x^8 / x^3
Simplify. 2^3 * 3^3
6^3
Is the square root of 16 rational or irrational?
Rational: The square root of 16 is a perfect square.
Write 0.433333... as a fraction.
39/ 90
Approximate the square root of 97. What numbers is it between?
Simplify. 2 ^ -3
1/8
Simplify. x^9 / x^4
x^5
Is the square root of 5 rational or irrational?
Irrational- The square root of 5 is not a perfect square
When do I multiply the original repeating decimal by 10? By 100? By both?
Multiply by 10: When 1 digit is repeating in the tenths place. The repeating decimal should be lined up
Multiply by 100: When both the tenths and the hundredths place are repeating
Multiply by 10 and 100: When the repeating decimal is only in the hundredths place
A cube has a volume of 64 cubic inches. What is the length of each side of the cube?
4 inches
x ^ (m/n)
What is n?
What is m?
N = denominator = root
M = numerator = power
A student says:
“Since 2^ -3 has a negative exponent, the answer must be negative.”
Is the student correct? Explain and simplify 2^-3
No. A negative exponent means to use the reciprocal. It does not mean the answer is negative.
1/8