1. Course 3, Lesson 1-10
Estimate to the nearest whole number.
1.
2.
3.
4.
5. Give two numbers that have square roots between 9
and 10.
39
102
71.3
25.9
8. Course 3, Lesson 1-10
The Number System
Words
Examples
Rational Number
A rational number is a
number that can be
expressed as the ratio ,
where a and b are integers
and b ≠ 0.
Irrational Number
An irrational number is a
number that cannot be
expressed as the ratio,
where a and b are integers
and b ≠ 0.
7
, -12
8
76-2,5,3. 1.414213562....2
9. 1
Need Another Example?
Step-by-Step Example
1. Name all sets of numbers to which the real
number belongs. 0.2525...
The decimal ends in a repeating pattern. It is a
rational number because it is equivalent to .
11. 1
Need Another Example?
Step-by-Step Example
1. Name all sets of numbers to which the real
number belongs. √36
Since √36 = 6, it is a natural number, a whole
number, an integer, and a rational number.
13. 1
Need Another Example?
Step-by-Step Example
1. Name all sets of numbers to which the real
number belongs. –√7
–√7 ≈ –2.645751311… The decimal does not
terminate nor repeat, so it is an irrational number.
15. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. Fill in the with <, >, or = to make a true statement.
√7 ≈ 2.645751311…
2 = 2.666666666…
Since 2.645751311… is less than 2.66666666…,
√7 < 2 .
17. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. Fill in the with <, >, or = to make a true statement.
15.7% √0.02
15.7% = 0.157
√0.02 ≈ 0.141
Since 0.157 is greater than 0.141, 15.7% > √0.02.
19. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
6. Order the set √30 , 6, 5 , 5.36 from least to
greatest. Verify your answer by graphing on a number line.
Write each number as a decimal. Then order the decimals.
√30 ≈ 5.48
5.36 ≈ 5.37
7
6 = 6.00
5 = 5.80
From least to greatest, the order is 5.36, √30, 5 , and 6.
20. Answer
Need Another Example?
3, √15, 4.21, 4
Order the set √15, 3, 4 , 4.21 from least to
greatest. Verify your answer by graphing on a
number line.
21. 1
Need Another Example?
2
3
4
Step-by-Step Example
7. On a clear day, the number of miles a person can see to the horizon is
about 1.23 times the square root of his or her distance from the ground in
feet. Suppose Frida is at the Empire Building observation deck at 1,250 feet
and Kia is at the Freedom Tower observation deck at 1,362 feet. How much
farther can Kia see than Frida?
Use a calculator to approximate the distance each person can see.
Frida: 1.23 • √1,250 ≈ 43.49
Kia can see 45.39 – 43.49 or 1.90 miles farther than Frida.
Kia: 1.23 • √1,362 ≈ 45.39
22. Answer
Need Another Example?
The time in seconds that it takes an object
to fall d feet is . About how many seconds
would it take for a volleyball thrown 32 feet
up in the air to fall from its highest point to
the sand?
1.4 s
23. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-10
The Number System
24. How did what you learned
today help you answer the
WHY is it helpful to write numbers in
different ways?
Course 3, Lesson 1-10
The Number System
Sample answer:
• Not all numbers can be written the same way. For
example, an irrational number cannot be written as an
integer.
25. Write one example of each of the following
•a whole number,
•an integer that is not a whole number,
•a rational number that is not an integer,
•an irrational number.
Ratios and Proportional RelationshipsThe Number System
Course 3, Lesson 1-10