Decimal Expansion
Exploring Irrational Numbers
Approximating Irrational Numbers
Comparing and Ordering
Problem Solving
100
Write - 4/3 as a decimal
-1.3333...
100
Is -3.22222.. rational or irrational? Why?
-3.222.. is rational because it is a repeating decimal.
100
Which two consecutive whole numbers is the square root of 33 between?
5 and 6
100
Which has a greater value? 47/7 or sqrt of 48
sqrt of 48
100
When x =5 and y = 6 is the expression sqrt(x^3 + y^2 + 7) rational or irrational? Explain
No, because when you add them together you get 168 and 168 is not a perfect square.
200
Write 68/9 as a decimal
7.555...
200
Is the square root of 45 rational or irrational?
The square root of 45 is irrational because it is not a perfect square.
200
Estimate the square root of 33 to the nearest tenth
5.7
200
Write the numbers in order from greatest to least. -2.7 -(sqrt of 5) -(2/7)
-(2/7), -(sqrt 5), -2.7
200
Benito wants to buy a car. He is considering two different models. Model A is 7 1/8 ft wide. Model B is 81 in wide. Express the width of each car in ft using a decimal. Which car is wider?
A - 7.125 ft <--- B - 6.75 ft
300
Write -31/10 as a decimal
-3.1
300
Is 7.2122122212221... rational or irrational?
Irrational because the same numbers are not repeating and it does not terminate.
300
Estimate the square root of 110 to the nearest tenth.
10.5
300
Write the numbers in order from least to greatest. 4.7 sqrt 19 sqrt 35 5.8
sqrt 19, 4.7, 5.8, sqrt 35
300
Find values for x and y to make the expression rational: sqrt(x^2 + y^2)
x = 3 y = 4
400
Write 0.81818181818181... as a fraction is simplest form.
9/11
400
Determine which of the following are irrational and explain why: -3/2 1.23242526 square root of 81 4.5555555..
None of these numbers are irrational. They can all be expressed as a fraction. The decimals are repeating or terminating and 81 is a perfect square.
400
The length of the car is the square root of 170 ft long. The garage measures 13 ft long. Will the car fit in the garage? Explain how you know.
The car will not fit in the garage because sqrt. of 170 is greater than 13. A car that is greater than 13 ft long will not fit in a garage of 13 ft.
400
Determine which expression has a great value: 12(sqrt 8) or 20(sqrt 3)
20(sqrt 3)
400
The area of a square poster 59 in^2. Find the length of one side of the poster to the nearest tenth
7.7 in.
500
Four fruit trees are being moved into an orchard. The trees are going to be placed from tallest to shortest. Write the height of trees in the order that they will be placed. 29/8 ft 10/3 ft 33/9 ft
10/3 ft 29/8 ft 33/9
500
Is the square root of 625 rational or irrational? How do you know?
Rational because 25 x 25 = 625
500
Estimate 4(sqrt.40)
25.2
500
Write the numbers in order from greatest to least. -2.7 -(31/10) -(sqrt 5), -0.9, -(2/7), -(sqrt 20)
-2.7, -0.9, -(sqrt 5), -2.7, -(31/10) -(sqrt 20)
500
After an accident, police can use the formula v = 2(sqrt 5L) to estimate the speed v, in miles per hour, that a car was traveling by measuring the length of the skid marks, L, in feet. Estimate the speed of a car that left skip marks 66 ft long. If the posted speed limit is 40 mi/h, was the car speeding?
36.4 mi/h The car was not speeding.
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