Download understand real numbers - White Plains Public Schools

“HOW TO” UNDERSTAND REAL NUMBERS:
Whole Numbers
Integers
0, 1, 2, 3, …
... -3, -2, -1, 0, 1, 2, 3, …
Rational Numbers
A rational number is any number written as a simple
fraction, or any decimal that repeats or terminates.
Examples:
0.25, 0.464646…, 25 ,
4
3
Irrational Numbers
An irrational number is a decimal that does not
repeat or terminate.
Examples:
2 , 10 , , 0.121121112…
TEST REVIEW QUESTIONS
1. Which is a rational number?
a)
b)
c)
d)
Explain why you think your choice is
correct?
19
49
29
π
_______ is rational b/c ____________
______________________________
2. Which number is irrational?
a) .75
b) .5
c) .323232
d) .123456…
______________________________
_______.
Explain why you think your choice is
correct?
_______ is irrational b/c __________
______________________________
______________________________
_______.
3. Which of the following is an
irrational number?
a)
b)
c)
d)
16
17
25
36
Explain why you think your choice is
correct?
_______ is irrational b/c __________
______________________________
______________________________
_______.
4. Which number is rational?
Explain why you think your choice is correct?
a)
b)
c)
d)
75
87
100
70
_______ is rational b/c ______________
_________________________________
____.
5. Which number is rational?
Explain why you think your choice is correct?
a) 
_______ is rational b/c _______________
b) 0.25
c)
7
d)
10
_________________________________
____.
6. Which number is an irrational number?
a)
2
Explain why you think your choice is correct?
4
b) 
3
_______ is irrational b/c _____________
_________________________________
____.
c) -1.8
d)  9
7. The set below contains only which type of numbers?
{–2, 6, 3½, 12, 1.25, 40, 64 , 200}
a) Mixed numbers
b) Rational numbers
c) Whole numbers
d) Counting numbers
Explain why you think your choice is correct?
_________ numbers are __________
______________________________
_______.
SQUARES AND SQUARE ROOTS
Perfect Squares – the product of a number times itself. Numbers that form
perfect square have equal side lengths. Perfect Squares represent the number of
squares needed to fill the inside of a square.
The Square Root of a Number A number which is multiplied by itself to give the
square number. It also represents the length of the side of a square.
SOLVE – NO CALCULATOR !!!!!
1. List the first fifteen perfect squares.
___, ___, ___, ___, ___, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____
2) List the next two perfect squares after 121:
________
________
3) Find the value of each:
64
________
225
_______
4) Find the value of n:
5) Which number below is a perfect square?
a)
a) 12
c) 81
n = 6
n = ________
b) 50
d) 90
Show your work or explain why:
b) n
2
= 49
n = _____ or ______
6) Between which two consecutive whole
numbers is 54 ?
7) Which number is irrational:
_______ and _______
Show your work or explain why:
25 or
75
______
Explain why:
8) Write the value for letters a and b shown on the number line:
9
6
b
a
a _________
b _________
(Write the value for b as a square root.)
9) Graph 15 on a number line and estimate to the nearest whole number.
You may use a calculator on the questions below!
10) n2 = 2601 n = ________ or _________
Show your work or explain how you found your answer:
11)
n = 29
n = ________
Show your work or explain how you found your answer:
12) Tim’s room is in the shape of a square. The room has an area of 225 ft2.
How long is each wall?
13) Anna’s room is square-shaped. The room has an area of 235 ft2.
How long is each wall? (Round your answers to the nearest tenth of a foot.)