Show:
Rewriting Rational Numbers
Describing Relationships of Rational Numbers
Ordering Real Numbers
Integer Exponents Properties
Scientific Notation
100
What is a good estimate for the solution to the equation x^3=95? How did you come up with your estimate?
Sample Answer: A good estimate is x equals approximately 4.5 because 4-cubed is 64 and 5-cubed is 125 and 95 is about halfway between 64 and 125, therefore, the cube root of 95 is probably closer to 4.5 than 4 or 5
100
Kate said, "Negative numbers are integers." What was her error?
The set of negative numbers also includes non-integer rational numbers and irrational numbers.
100
Order the following numbers from least to greatest: 1. square root of 7, 2, (square root of 8) divided by 2 2. square root of 10, pi, 3.5 3. square root of 220, -10, square root of 100, 11.5
1. (square root of 8) divided by 2, 2, square root of 7 2. pi, square root of 10, 3.5 3. -10, square root of 100, 11.5, square root of 220
100
Explain why the exponents cannot be added in the product 12^3 x 11^3.
The exponents cannot be added because the bases are not the same.
100
If you were a biologist counting very large numbers of cells as part of your research, give several reasons why you might prefer to record your cell counts in scientific notation instead of standard notation.
Scientific notation is shorter to write, easier to read (you see how many zeros), used by scientists everywhere, and easier to compare sizes of large numbers.
200
A 7/16 inch-long bolt is used in a machine. What is the length of the bolt written as a decimal?
0.4375 inches
200
Irrational Numbers can never be precisely represented in decimal form. Why is this?
In decimal form, irrational numbers never terminate and never repeat. Therefore, no matter how many decimal places you include, the number will never be precisely represented. There are always more digits.
200
Approximate a real number between the square root of 13 and the square root of 14
Sample answer: 3.7
200
A student claims that 8^3 x 8^-5 is greater than 1. Explain whether the student is correct or not.
The student is not correct because the answer is 1/ 64 which is less than 1.
200
A single brown bat can eat up to 1,000 mosquitos in a single hour. Express in scientific notation how many mosquitos a little brown bat might eat in 10.5 hours.
1.05 x 10^4
300
Can you find the cube root of a negative number? If so, is it positive or negative? Explain your reasoning.
Yes, the cube root of a negative number is negative, because a negative number cubed is always negative, and a nonnegative number cubed is always nonnegative.
300
Write all names that apply to the following numbers: 1. square root of 9 2. square root of 50 3. 16.6 4. 8 1/2 5. 257 6. square root of 16
1. whole, integer, rational, real 2. irrational, real 3. rational, real 4. rational, real 5. whole, integer, rational, real 6. whole, integer, rational, real
300
Approximate an irrational number between 5 and 7.
Sample answer: square root of 31
300
A student simplified (6^2)/(36^2) as 1/3. Do you agree with this student? Explain why or why not.
No, this equals 1/36.
300
A graphing calculator displays 1.89 x 10^12 as 1.89E12. How do you think it would display 1.89 x 10^-12? What does "E" stand for?
1.89E-12, the exponent of 10
400
A baseball pitcher has pitched 98 2/3 innings. What is the number of innings written as a decimal?
98.6 repeating
400
Which set of numbers best describes the following situations: 1. the height of an airplane as it descends to an airport runway 2. the score with respect to par of several golfers: 2, -3, 5, 0, 1
1. real numbers- the height can be any number greater than zero 2. integers, the scores are counting numbers, their opposites, and zero
400
Jill says 12.6 repeating is less than 12.63. Explain her error.
She did not consider the repeating digit 12.6666666...
400
A number to the 12th power divided by the same number to the 9th power equals 125. What is the number?
The number is 5
400
The volume of a drop of a certain liquid is .000047 liter. Write the volume of the drop of liquid in scientific notation.
4.7 x 10^-5
500
There are 26.2 miles in a marathon. Write the number of miles as a fraction.
26 1/5 miles
500
Ronald states that the number 1/11 is not rational because when converted into a decimal, it does not terminate. Nathaniel says it is rational because it is a fraction. Which boy is correct? Explain.
Nathaniel is correct. A rational number is a number that can be written as a fraction, and 1/11 is a fraction.
500
There is a famous irrational number called Euler's number, symbolized with an e. Like pi, its decimal form never ends or repeats. The first few digits of e are 2.7182818284. a) Between which two square roots of integers could you find this number? b) Between which two square roots of integers can you find pi?
a) between square root of 7= approximately 2.65 and square root of 8= approximately 2.83 b) between square root of 9= 3 and square root of 10= approximately 3.16
500
Write equivalent expressions for x^7 times x^-2 and (x^7)/(x^2). What do you notice? Explain how your results relate to the rules of integer exponents.
Bot expressions equal x^5. When multiplying powers with the same base, you add exponents. When dividing powers with the same base, you subtract exponents.
500
The U.S. public debt as of October 2010 was $9.06 x 10^12. What was the average U.S. public debt per American if the population in 2010 was 3.08 x 10^8 people?
What is $2.94 x 10^4, or $29,400 per person.