1. Write each fraction as a decimal.
Warm Up
Simplify each expression.
1. 62
2. 112
121 36 49 81 4. 72
Write each fraction as a decimal. 2 5 5 9 5.
0.4 6.
0.5

2. Estimating Rational Numbers
Mrs. Long

3. Objectives: In this lesson you’ll:
Estimate and compare rational and irrational numbers 3

4. Words to know…
Square root - a number which, when multiplied by itself, produces the given number. (Ex. 7² = 49, 7 is the square
root of 49)
Perfect square- any number that has an integer square root.(ex. 100 is a perfect square ,

5. Square Roots Perfect Square Roots Squares 0² = 0 1² = 1 2² = 4 3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Perfect Square Roots

6. Writing Math
The small number to the left of the root is the index. In a square root, the index is understood to be 2. In other words, is the same as .

7. You try Find each root. Think: What number squared equals 81?
= –6
(–6)(–6)(–6) = 36(–6) = –216

8. You try Finding Roots of Fractions. Think: What number squared equals

9. You try Finding Roots of Fractions. Think: What number squared equals
= –6
(–6)(–6)(–6) = 36(–6) = –216

10. Approximating Square Roots
Square roots of numbers that are not perfect squares, such as 15, are not whole numbers. A calculator can approximate the value of as Without a calculator, you can use square roots of perfect squares to help estimate the square roots of other numbers.
If a whole number is not a perfect square, then its square root is irrational. For example, 2 is not a perfect square and is irrational.
Remember

11. Approximating Square Roots
Approximate to the nearest whole number.
Solution
Is between 7² and 8².

12. Let’s practice… Between 2 and 3 Between 4 and 5 Between 4 and 5
Determine what two consecutive integers each root lies between.
Between 2 and 3
Between 4 and 5
Between 4 and 5
Between 5 and 6

13. Great Job!!! You are soooo AWESOME!

14. Words to know…
Natural numbers - The counting numbers. (example: 1, 2, 3…)
Whole numbers - The natural numbers and zero.(example: 0, 1,2,3…)
Integers -The whole numbers and their opposites.(ex: …-3,-2,-1,0,1,2,3…)
Rational numbers - Numbers that can be expressed as a fraction (a/b).

15. Words to know…
Terminating decimal -Rational numbers in decimal form that have finite (ends) number of digits. (ex 2/5= 0.40 )
Repeating decimal -rational numbers in decimal form that have a block for one or more digits that repeats continuously. (ex. 1.3= )
Irrational numbers - numbers that cannot be expressed as a fraction including square roots of whole numbers that are not perfect squares and nonterminating decimals that do not repeat.

16. The real numbers are made up of all rational and irrational numbers.
Note the symbols for the sets of numbers.
R: real numbers
Q: rational numbers
Z: integers
W: whole numbers
N: natural numbers
Reading Math

17. Classifying Real Numbers
Write all classifications that apply to each real number. A.
–32 32 1
–32 can be written in the form .
–32 = –
–32 can be written as a terminating decimal.
–32 = –32.0
rational number, integer, terminating decimal B.
14 is not a perfect square, so is irrational.
irrational

18. Write all classifications that apply to each real number.
Check It Out!
Write all classifications that apply to each real number.
7 can be written in the form .
4 9
a. 7
can be written as a repeating decimal.
67  9 = 7.444… = 7.4
rational number, repeating decimal
b. –12
–12 can be written in the form .
–12 can be written as a terminating decimal.
rational number, terminating decimal, integer

19. Write all classifications that apply to each real number.
10 is not a perfect square, so
is irrational.
irrational
100 is a perfect square, so is rational.
10 can be written in the form and as a terminating decimal.
natural, rational, terminating decimal, whole, integer

20. A challenge…
Would you know how to solve this….
-11
-11
x = 5

21. A challenge…
Solve the variable. -3 -3
x = 8