Download Natural Whole Integer Choose only one: Real Rational Irrational 0 5

1.7 Practice The Real Numbers System
1. Circle irrational numbers in the list: –2, –√
2.
, 0, –0.3,
–√
, √
,
, 7.010203…
Choose the starting point, and then move toward “Real”
Natural
Whole
Integer
(counting
numbers:
1, 2, 3, …)
(and ZERO)
(and
negatives)
NO DECIMAL PART
Choose only one:
Rational
Irrational
(N, W, Z, AND
repeating or
terminating,
decimal part)
(OR non-terminating,
non-repeating
decimal part)
DECIMAL PART
0
5
-9
√
√
0.141414…
0.010110111…
Name all sets of numbers to which each real number belongs.
1. 12
2. –15
3. 1
4. 3.18
5.
6. 9. ̅
7. – 2
8. √
9. √
10. – √
11. – √
12. 5.78791…
13. 3.589589…
14.
15.
16. Estimate the solution of a² = 21 to the nearest tenth.
Real
(all of
them)
Determine whether a given number is a member of a particular subset. Some numbers may appear more
that in one subset:
–√
, 5.37373…, 32,
, −2 , 0 , 2.31, −1.9502…
Natural numbers: __________________
Whole numbers: ___________________
Integers: ___________________
Rational Numbers: _________________
Irrational numbers: __________________
Real numbers: _____________________
21. The area of a square painting is 600 square inches. To the nearest hundredth inch, what is the side of the
painting? To the nearest hundredth inch, what is the perimeter of the painting?
22. Determine whether each statement is sometimes, always, or never true. Give an example to prove your answer.
a) A decimal is an irrational number.
b) An integer is a whole number.
c) A natural number is an rational number.
d) A negative integer is a natural number.
23. Estimate each square root to the nearest tenth. Then graph the square root on a number line.
√
√
√
Challenge In Exercises 17– 20, evaluate the expression when x = –1, x = 0, and x = 1. Then determine whether the
result is a whole number, an integer, or a rational number (most precise name).
x2  1
24. x  3
25.
x
x2  2
1 x
26. x 2  1
27.
x2  2
x3  2