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Rational Numbers
Powers and Exponents
Scientific Notation
Roots
Comparing Rational Numbers
100
This is the decimal equivalent for 2 and 16/25.
What is 2.64? How? Leave the 2. Divide the numerator by denominator.
100
Rewrite 8 x 8 x 8 x 8 using exponents.
What is 8 to the fourth power (8 with a small four)?
100
This is why we use scientific notation?
What is to make it easier to write REALLY LARGE OR REALLY SMALL NUMBERS.
100
Find the square root of 49.
What is 7? Why? 7 x 7 = 49. A square root is the inverse of the square.
100
What number sets does the square root of 2 belong too? Choices: natural, Whole, integers, rational, irrational, real
What is Irrational and Real? Why? The square root of 2 equals a non-terminating decimal point making it irrational versus a rational number. It is not a counting (natural), whole, or integer.
200
This is the decimal equivalent for -2/3.
What is .6666666......? How? Divide numerator by denominator.
200
Simplify: 4 to the negative 2nd power x 4 to the third power
What is 16? How? 4 x 4 = 16 and when you multiply exponents, ou add them, so -2 plus 3 = 1 So the answer is 16 to the first power which is just 16.
200
Write in standard notation: 9.2478 x 10 to the fifth power
What is 924,780? How? Multiply 9.2778 by (10 x 10 x 10 x 10 x 10), or realize that this moves the decimal to the right five times.
200
What is the cube root of 64?
What is 4? Why? 4 cubed is 4 x 4 = 16 x 4 = 64
200
What numbers sets does -19 belong to? Choices: natural, Whole, integers, rational, irrational, real
What is Integers, Rational and Real?
300
Find the fraction equivalent for 0.8. Make sure it is simplest form.
What is 4/5? How? 0.8 = 8/10 = divide by the GCF (2) = 4/5
300
Simplify . Express using positive exponents. h to the negative 2nd power divided by h to the 4th power.
What is 1/h to the 6th power? How? h/h = h and when you divided exponent you subtract the denominator FROM the numerator. This would be -2 - 4 which equals -6. Now we have h to the negative 6th power so we have to rewrite it as 1/h to the 6th power (so it is positive)
300
Write in scientific notation: 0.0000581
What is 5.81 x 10 to the negative 5th power? Why? A number in Scientific Notation must be within 1 and 10, so the decimal must move over to the right of 5. THis caused the decimal to move 5 times to the right making the number appear 500, 000 time bigger (or 10 to the fifth). The negative represents that the number is actually worth 500,000 less. A negative exponent moves the decimal to the left.
300
Find the square root of -25.
What is "not possible"? You cannot find a square root of a negative number.
300
Which is greater? 4 and 1/6 or the square root of 17?
What is 4 and 1/6? Why? 4 and 1/6 = 4.16 Sq root of 17 = 4. 12
400
Write 1.77777 .... as a mixed number in simplest form.
What is 1 and 7/9? How? A. First think how many digits repeat? Just the 7 so 1 digit.B. Multiply by 10 (1 zero) on both sides. 10N = 10 (1.7777) C. So this equals 10N = 17.7777 D. Subtract 1N which is 1.777 So now you have 9N = 16. E. Divide by 9: so N=16/9
400
Evaluate the expression 5 to the negative 1st power
What is 1/5 which equals .20? (One over 5 to the 1st power) Why? Any nonzero number to the negative n power is the multiplicative inverse of the number to the nth power.
400
Evaluate: 5.46 x 10^5 divided by 8.4 x 10^3
What is How: A. Divide the Decimal Numbers (5.46/8.4) = 0.65 B. Recall Exponent rules: When dividing exponents, you subtract (5-3) = 2 C. Now we have 0.65 x 10^2. D. We must move the decimal over one place to the right. That would make it 6.5 x 10
400
Solve the equation x^2 = 3,600
What is 60? Why? To undo a square you find the square root. So we need to find the square root of 3,600. I know 6x6 = 36. So I try 60x 60.
400
Which is greater? 3.31 or square root of 11
What is the square root of 11? WHy? square root of 11 = 3.316 which is 6 thousandths greater than 3.31
500
This is a Scientific Notation Problem.... Recently in the US, there were about 300,000,000 cell phone users. That same year, there were 5.7 x 10^9 cell phone users worldwide. About how many times larger was the number of cell phone users worldwide than in the US?
What is 19 times larger? How? This is a division problem. Set it up how the problem asks: Worldwide users/US users. 5.7 x 10^9 divided by 300,000,000 (3 x 10^8) Now follow the rules. (5.7 / 3) and Subtract Exponent (9-8) = 1.9 x 10 (to the first power). = 19
500
Write the expression using a positive exponent: 10 to the negative 3rd power
What is 1/10 to the third (one over ten to the third) Why? Any nonzero number to the negative n power is the multiplicative inverse of the number to the nth power.
500
Evaluate (4.3 x 10^4) + (5.21 x 10^5)
What is 5.64 x 10^5? How? A. Make sure exponents are equal. If not, change one. I will change the power of 4 to a power of 5. I have to move the decimal accordingly. So 4.3 x 10^4 becomes .43 x 10^5. B. Add the decimal numbers. Exponents stay the same. .43 + 5.21 = 5.64
500
Estimate the square root to the nearest integer. Square root of 41
What is 6? How? I think of what I know around 41. I know that 6 squared is 36 and 7 squared is 49, so the square root of 41 is between 6 and 7. Now which is closest? 41 is 5 more than 36 and 8 less than 49. We are closer to 41.
500
Order from least to greatest: (square root of 7, negative square root of 8, 4 and 1/7, -4
What is -4, negative square root of 8, sq root of 7, 4 and 1/7? Why? -4 square root of 7 = 2.645 neg sq root of 8 = -2.828 4 and 1/7 = 4.142