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Fractions and Decimals

Agenda March 24, 2009 (Week 11)

Take your folder, remove your homework.

Write the submitted homework number on the
inside cover with your new homework

Section 3-5 Fractions and Decimals, and the
volume of a Sphere

Section 3-6 Square Roots and Pythagorean
Theorem

Reminder: bring notebook everyday to this class

3-5 Fractions and Decimals, and the Volume of a Sphere

Objective:
Convert fractions to decimals
Convert decimals to fractions
Simplify expressions containing fractions and
decimals
Solve applications involving fractions and decimals

Converting fractions to decimals
Examples: Write ¾, 3/5 as decimal
Examples: repeated decimals 11/12, 5/11

Converting decimals to fractions
Examples: write 0.38, 0.48, 0.75, 0.025, 12.8 as a fraction in
lowest terms
Examples: write 15.6, and 12.8 as a mixed number

Problems involving both Fractions and Decimals

Simplify (19/50)(1.32+0.48)

Simplify (14/25)(2.43+0.27)

Simplify 1/4 + (0.25)(3/5)

Simplify (1/2)³(2.4)+(1/4)²(3.2)

Applications:
If a shirt that normally sells for $27.99 is on sale for 1/3 off, what
is the sale price of the shirt?
Find the area of a triangular stamp with base 2 and 5/8 inches,
and height = 1 and ¼ inches.

The volume of a sphere is (4/3)π(radius)³ = (4/3)πr³
A figure is composed of a right circular cylinder with half
a sphere on top. (a half-sphere is called a hemisphere)
find the volume of this figure with radius = 5 inches,
height = 10 inches, round to the nearest tenth

Guided Practices and Homework # 22

To convert fractions to decimals, do we multiply or divide
the numerator by the denominator?

The decimal 0.13 is equivalent to what fractions?

Write 36 thousandths in decimal form and in fraction
form

Explain how to write the fraction 84/1,000 in lowest terms.

Homework # 22, pp 265-270, #1-7 odd, 9-49 EOO, 51-
87 EOO.

3.6 Square Roots and the Pythagorean Theorem

Objective: Find square roots of numbers

Use decimals to approximate square roots

Solve problems with the Pythagorean Theorem

Definition: if b²= a, then , and is read as b is the
square root of a. The symbol is called radical symbol,
and a is called radicand.

Examples of square roots on the board.

Simplify a radical expression means to remove perfect
square from the radicand

Examples of simplifying the radical expression on the
board and approximations

Facts from Geometry: The Pythagorean Theorem

A right triangle is a triangle that contains a 90°(or right)
angle. The longest side in a right triangle is called the
hypotenuse, we use the letter c to denote it. The two
shorter sides are denoted by the letter a and b (they are
called legs)

The Pythagorean Theorem stated that c²= a² + b²
Applications of Pythagorean Theorem, examples on
the board

A ladder is leaning against the top of a 6-foot wall. If the
bottom of the ladder is 8 feet from the wall. How long is
the ladder?

Example of Spiral of roots

8Guided Practices and Homework # 23

Which number is larger, the square of 10 or the
square root of 10?

Give a definition for the square root of a number?

What two numbers will the square root of 20 fall
between?

What is the Pythagorean Theorem?

Homework #23, page 277-282, # 1-39, # 41-45
ODD, # 47-63 EOO, 67-75 ODD

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