Scientific Notation, Exponent Laws, Rational and Irrational

Scientific Notation and Exponent laws and Rational and Irrational Numbers

By Grace Howard

• Pi

• Radical (non- perfect square)

• Decimal with no repeating pattern

Irrational

• Perfect Square Root

• Terminating or Repeating Decimal

• can be a Fraction

​Rational

Classify Numbers

Multiple Choice

What type of number is π ?

• Rational
• Irrational

Multiple Choice

Which number is irrational?

• 9.6
• √45
• 3/8
• 3.4 x 10 ⁵

Multiple Choice

Which number is a rational number ?

• 1/4
• π
• √3
• ∛25

Multiple Choice

.141414141414...

• Rational 
• Irrational 

Multiple Choice

A terminating decimal is a decimal that...

• Never ends

• repeats a pattern

• ends

• never ends and never repeats

​Standard to Scientific Notation

If the number is bigger then 1, move the decimal to the left, the exponent is positive

If the number is smaller then 1, move the decimal to the right, the exponent is negative

Multiple Choice

How would you write 564,000,000 in scientific notation?

• 5.64 x 10^-7
• 5.64 x 10⁶
• 5.64 x 10⁸
• 56.4 x 10⁷

Multiple Choice

Express the following in scientific notation:
.000457

• 457 x 10⁶
• 457 x 10^-6
• 4.57 x10⁴
• 4.57 x 10^-4

Multiple Choice

What is 7.0 x 10^-5 in standard form? 

• .0007
• .00007
• .000007
• .0000007

Multiple Choice

How do you write
8.317 x 10⁶
in standard form?

• 8, 371, 000
• 83, 170, 000
• 837, 100
• 8, 317, 000

​Word Problems- Key Words

Divide

• How many times smaller/larger/greater

• average

Subtract

• How many more

• Difference

Add

• Sum

• Combined

• Multiply- is based on context
  

Multiple Choice

4. Find the combined mass of Earth and Venus. Earth is approximately 5.9 x 10²⁴ kg and Venus is approximately 4.9 x 10²⁴ kg.

• Add
• Subtract
• Multiply
• Divide

Multiple Choice

3. In the year 2000, the United States public debt was about 5.6 x 10¹² dollars.  The population of the United States in that year was about 2.8 x 10⁸ people.  What was the average debt per person?

• Add
• Subtract
• Multiply
• Divide

Multiple Choice

2. On average, Mercury is about 57,000,000 km from the sun, whereas Neptune is about 4.5 x 10^9 km from the sun. What is the difference between Neptune’s and Mercury’s distances from the sun?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

5. The Colorado Department of Education spent about 4.408 x 10⁹ in fiscal year 2004-2005 on public schools.  There were about 7.6 x 10⁵ students enrolled in public school.  What was the average spending per student? 

• Add
• Subtract
• Multiply
• Divide

Multiple Choice

The mean distance from the sun to Earth is 9.29 x 10⁷ miles. Jupiter's mean distance from the sun is 4.8388 x 10⁸ miles. What is the difference between these two distances in miles?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

The mass of he sun is 1.989 x 10³⁰ kilograms. The mass of the earth is 5.98 x 10²⁴ kilograms. How many times bigger is the sun than the earth?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

By area, Russia is the largest country in the world. It has an area of 8.649 x 10⁶ square miles. Canada is second with 4.797 x 10⁶ square miles. What is the difference in area?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

A factory can make 3 × 10⁴ t-shirts per day, how many t-shirts will it make in 2.5 ×10² days?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

The mass of he sun is 1.989 x 10³⁰ kilograms. The mass of the earth is 5.98 x 10²⁴ kilograms. How many times bigger is the sun than the earth?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

The population of Mathville is 5.6 x 10³. The population of Algeville is 1.3 x 10⁴. How many more people are there in Algeville?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

In 1985 Earth had 4.9 ×10⁹ people living on it and in 2005, earth had 6.4 ×10⁹ living on it. How many more people inhabited Earth in 2005 than in 1985?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

If a computer can perform an addition operation in 1.5 x 10^-6 seconds, how long will it take to perform 1500 such operations?

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

A TV show had 3.5 × 10⁶ viewers for their first episode and 8.5 × 10⁶ viewers for their second episode. How many viewers did they have overall?

• Add

• Subtract

• Multiply

• Divide

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Law of Exponents

Quotient Rule

When dividing exponents with the same base

Power Rule

• To raise a power to a power, multiply the powers

• Ex. 1: (4³)²=

• Ex. 2: (3⁵)⁶=

• Ex. 3: (p⁴)³ =

Product Rule

• To multiply exponents with the same base, add the exponents

• Ex. 1: 5³ x 5⁴ =

• Ex. 2: 1,000² x 1,000³ =

• Ex. 3: y⁵ x y³ =

Zero Exponent Rule

• Anything raised to the 0 power is 1

• Ex. 1: 4⁰=1

• Ex. 2: 1,000⁰=1

• Ex. 3: x⁰=1

Negative Exponents...

Multiple Choice

Evaluate this expression using the quotient rule.

• 9⁵
• 9⁹
• 1⁵
• 9^-5

Multiple Choice

Make this negative exponent positive.
9^-3

• 9³
• 1/9^-3
• 1/9³
• 729

Multiple Choice

Simplify:
b² ⋅ b⁴

• b⁸
• b⁶
• b²
• 2b⁶

Multiple Choice

Simplify:
(x⁵)⁴

• x⁹
• x²⁰
• x
• x⁵⁴

Multiple Choice

(x³y)⁶

• 2x¹⁸y⁶
• x¹⁸y⁶
• x³y⁶
• x³y⁶

Multiple Choice

Simplify (-1/2)⁰

• 1
• 0
• -1
• -2

Multiple Choice

Simplify the following expression: 
xy^-7

• xy⁷
• x/y⁷
• x⁷/y
• x⁷y

Multiple Choice

• a⁷
• a¹⁰
• a³
• a^-3

Multiple Choice

Simplify:

• x⁶y⁴

• x²y⁴

• x⁸y⁴

• x⁸y

Multiple Choice

Anything raised to a power of zero is always: 

• 0
• 1
• itself
• negative

Multiple Choice

Simplify the expression using exponential notation:

$$a^2\cdot a^4$$  

• $$a^6$$  

• $$a^8$$  

• $$a^2$$  

• $$a^{24}$$  

Multiple Choice

Simplify the expression using exponential notation:

$$\frac{m^5n^6}{m}$$  

•   $$m^6n^6$$  

• $$m^4n^6$$

• $$m^3n$$  

• $$mn$$