Real Number System
Classify 7 into all of the real-number subsets to which it belongs.
Natural, Whole, Integer, Rational, and Real.
Between which two consecutive integers does
\sqrt{35}
lie
5<\sqrt{35}<6
Which is greater?
\sqrt{25}\quad\text{or}\quad4.8
\ \sqrt{25}
A price increases from $50 to $60. What is the percent increase?
20% increase
A restaurant bill is $40. What is a 15% tip?
$6.00
Is 0.272727 rational or irrational? Explain briefly
Rational. It is a repeating decimal, so it can be written as a fraction
Which integer lies between
\sqrt{13} and \sqrt{24}?
4
0.62,\qquad \frac3 5,\qquad0.59
Arrange from least to greatest:
0.59,\ \frac3 5,\ 0.62
A quantity decreases from 80 to 68. What is the percent decrease?
15% decrease
An item costs $75 before tax. The sales-tax rate is 6%. What is the total cost after tax?
$79.50
Classify
-\sqrt{81
into all applicable real-number subsets
-\sqrt{81}=-9
So it is an Integer, Rational Number, and Real Number
Estimate
\sqrt{58}
to the nearest tenth
7.6
Arrange from least to greatest:
\pi,\ \sqrt{10},\ 3.2
\pi,\ \sqrt{10},\ 3.2
The price of an item increases from $240 to $282. What is the percent increase?
17.5% increase
A restaurant bill is $52.40 before tip. What is an 18% tip, rounded to the nearest cent?
$9.43
Which number is irrational?
\frac{-7}{4},\qquad \sqrt{50},\qquad 0.125,\qquad 0.333\ldots
sqrt 50
Which expression has a value between 12 and 13?
A. \sqrt{115} B. \sqrt{130} C. \sqrt{170} D. \sqrt{185}
\sqrt{130}
least to greatest:
72\%,\qquad\frac3 4,\qquad\sqrt{0.64},\qquad0.73
72\%,\ 0.73,\ \frac3 4,\ \sqrt{0.64
A reservoir begins with 500 million gallons of water. During the month, 130 million gallons enter and 80 million gallons are released. What is the percent change from the beginning to the end of the month?
10% increase
A meal costs $68.50 before tax and tip. Sales tax is 6%, and the customer leaves a 20% tip based on the pre-tax bill. What is the final total?
$86.31
Which two statements are always true?
A. Every integer is rational.
B. Every rational number is an integer.
C. Every irrational number is real.
D. Every square root is irrational.
A. Every integer is rational.
C. Every irrational number is real.
Without immediately using a calculator, estimate
\sqrt{85}
to the nearest tenth and explain why your answer is reasonable
9.2
Since 85 is much closer to 81 than to 100, the value should be a little greater than 9.
Arrange from least to greatest:
-\frac9 4,\ -\sqrt5,\ -220\%,\ -2.1
-\frac9 4,\ -\sqrt5,\ -220\%,\ -2.1
A stock starts at $72, drops to $54, and later rises to $63. What is the overall percent change from its original price?
12.5% decrease
A meal costs $58 before tax. Sales tax is 6%. The customer leaves a tip based on the pre-tax bill and pays $79.46 total. What percent tip did the customer leave?
31%