4/27 Pre Algebra Review

Scientific Notation is a way to write very large and small numbers using powers of 10.

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Scientific Notation

​The larger the exponent, the bigger the number.

Multiple Choice

If the exponent on the power of 10 is a positive number...

• you will get a large number that is greater than 1

• you will get a smaller number that is less than 1

Multiple Choice

Which of the following numbers is written in correct scientific notation?

• $$64.2\cdot10^2$$  

• $$6.42\cdot10^3$$  

• $$0.642\cdot10^4$$  

• $$6240$$  

Multiple Choice

Which of these numbers is the smallest?

• 3.5 x10⁷

• 3 x10⁸

• 5 x10⁷

• 5.5 x10⁶

Dropdown

To compare two numbers that are in scientific notation, first compare the​

Select answer

. If they are the same, then compare the​

Select answer

.​

Multiple Choice

Which of these numbers is the greatest?

• 9 x 10⁹

• 8.1 x10¹⁰

• 9.02 x10⁹

• 6.35 x10¹⁰

For any numbers that are less than 1, we write the number using a positive power of 10​.

The larger the number, the greater the exponent.

Scientific Notation: How to

For any numbers that are greater than 1, we write the number using a positive power of 10​.

The larger the number, the greater the exponent.

Scientific Notation: How to

Multiple Choice

How is the following number written in scientific notation?

450,000

• 4.5  x  10⁵

• 45  x  10⁵

• 4.5  x  10⁴

• 4.5  x  10⁶

Multiple Choice

How is the number below written in scientific notation?

0.000398

• 39.8  x  10^-5

• 3.98  x  10^-5

• 3.98  x  10^-4

• 39.8  x  10^-6

Multiple Choice

Which of the following is the correct way to write 3.97  x  10^-2 in standard form?

• 0.000397

• 0.0397

• 0.0000397

• 0.397

Multiple Choice

Which is the correct way to write the number 3.5 x 10⁶  in standard notation?

• 0.0000035

• 35,000,000

• 3,500,000

• 0.00000035

Multiple Choice

7.82 x 10^-6 is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

• Large

• Small

• Basic

Multiple Choice

7.82 x 10^-6 is an example of scientific notation. The exponent of -6 tells you your number will be very ________.

• Large

• Small

• Basic

Multiple Choice

Change from standard form to scientific notation: 12,000,000

• 12.0  x  10⁷

• 0.12  x  10⁷

• 1.2  x  10⁶

• 1.2  x  10⁷

Multiple Choice

Change from standard form to scientific notation:  450,000

• 4.5  x  10⁵

• 45  x  10⁵

• 4.5  x  10⁴

• 4.5  x  10⁶

Multiple Choice

Change from standard form to scientific notation:  0.000398

• 39.8  x  10^-5

• 3.98  x  10^-5

• 3.98  x  10^-4

• 39.8  x  10^-6

Multiple Choice

Change from standard form to scientific notation: 0.004078

• 4.078  x  10^-3
• 4.078  x  10³
• 40.78  x  10^-4
• .4078  x  10^-2

Multiple Choice

125,678,000: Change to scientific notation

• 1.25678  x  10¹²

• .125678  x  10^-9

• 12.5678  x  10⁸

• 1.25678  x  10⁸

Multiple Choice

Try to change the number back to standard form:  6.79  x  10⁴

• 679,000

• 6,790

• 67,900

• 6,790,000

Multiple Choice

Try to change the number back to standard form: 3.97  x  10^-2

• 0.000397

• 0.0397

• 0.0000397

• 0.397

Multiple Choice

The factor multiplied by a power of 10 in scientific notation needs to be greater than or equal to one but less than ___________?

• 1

• 10

• 100

• 1,000

Multiple Choice

How would you write 0.0005 in scientific notation?

• 50 x 10⁵

• 5 x 10⁴

• 5 x 10³

• .5 x 10³

Multiple Choice

How would you write -5.6 x 10^-3 in standard form?

• 0.0056

• -5,600

• 0.00056

• -0.0056

Multiple Choice

The rule of scientific notation is to write all exponents with a base of ____.

• 50

• 5

• 100

• 10

Multiple Choice

Which of the following in the LARGEST number?

• 9 x 10⁶

• 8 x 10¹⁰

• 1.3 x 10¹²

• 5.3 x 10³

Multiple Choice

Which of the following numbers is the SMALLEST?

• 8.7 x 10³

• 3 x 10⁴

• 1.3 x 10⁸

• 9 x 10²

Multiple Choice

Order the following from greatest to least:
 5 x 10³ 
 3.2 x 10⁸
 1.2 x 10⁸
 7 x 10⁵ 

•  7 x 10⁵ ,  5 x 10³ ,  3.2 x 10⁸,  1.2 x 10⁸

•  3.2 x 10⁸, 1.2 x 10⁸,  7 x 10⁵, 5 x 10³ 

•  1.2 x 10⁸, 3.2 x 10⁸,  5 x 10³ , 7 x 10⁵ 

Multiple Choice

Place the following numbers in order from least to greatest:

7.8 x 10⁶, 5.1 x 10⁴, 1.25 x 10⁵, 4.09 x 10⁴

• 4.09 x 10⁴,

  1.25 x 10⁵,

  5.1 x 10⁴,

  7.8 x 10⁶

• 4.09 x 10⁴,

  5.1 x 10⁴,

  1.25 x 10⁵,

  7.8 x 10⁶,

• 1.25 x 10⁵,

  4.09 x 10⁴,

  5.1 x 10⁴,

  7.8 x 10⁶,

Multiple Choice

The diameter of the planet Mercury is

4.87 x 10³ km. The diameter of the planet Venus is 1.21x10⁴ km. The diameter of the planet Mars is 1.28 x 10³ km.

Which planet has the smallest diameter?

• Mercury

• Mars

• Venus

Multiple Choice

Order the following from

greatest to least:

5 x 10³

3.2 x 10⁸

1.2 x 10⁸

7 x 10⁵

• 7 x 10⁵ , 5 x 10³ , 3.2 x 10⁸, 1.2 x 10⁸

• 3.2 x 10⁸, 1.2 x 10⁸, 7 x 10⁵, 5 x 10³

• 1.2 x 10⁸, 3.2 x 10⁸, 5 x 10³ , 7 x 10⁵

Multiplication and Division of Scientific Notation

Unit 1 - Lesson 3

Multiplication in Scientific Notation

BUT FIRST...

Multiple Choice

$$Simplify:\ 3x^2\ \cdot\ 4x^5$$  

• $$7x^7$$  

• $$12x^7$$  

• $$7x^{10}$$  

• $$12x^{10}$$  

Remember when multiplied powers?

First we MULTIPLY the coefficients and then we apply the product rule:

When you multiply powers with the same base you keep the base and ADD the exponents

What about scientific notation?

Actually its exactly the same thing!!

Multiple Choice

$$Simplify:\ 3\times10^2\ \cdot\ 4\times10^5$$  

• $$7\times10^7$$  

• $$12\times10^{10}$$  

• $$7\times10^{10}$$  

• $$12\times10^7$$  

Multiple Choice

Solve:

(2.1×10​²​​) × (3.0×10​⁴)

• 5.1 x 10²

• 6.3 x 10⁶

• 5.1 x 10⁶

• 6.3 x 10⁸

Multiple Choice

Multiply:
(-3 x 10⁵)(1 x 10^-2)

• 3 x 10³

• 3 x 10⁷

• -3 x 10³

• -3 x 10^-10

Multiple Choice

Multiply:
(2 x 10^-9)(-4 x 10^-8)

• 8 x 10^-17

• 8 x 10^-1

• -8 x 10¹⁷

• -8 x 10^-17

Multiple Choice

Find the product. Write your answer in proper scientific notation.

(5 x 10⁶)(3 x 10⁸)

• 15 x 10¹⁴

• 1.5 x 10¹⁴

• 1.5 x 10¹⁵

• 1.5 x 10¹³

Division in Scientific Notation

BUT FIRST...

Multiple Choice

$$Simplify:\ \frac{6x^8}{2x^4}$$  

• $$3x^4$$  

• $$4x^4$$  

• $$3x^2$$  

• $$4x^2$$  

Remember when we divided powers?

First we DIVIDE the coefficients and then we apply the quotient rule:

When you divide powers with the same base you keep the base and SUBTRACT the exponents

Multiple Choice

$$Simplify:\ \frac{6\times10^8}{2\times10^4}$$  

• $$3\times10^2$$  

• $$4\times10^4$$  

• $$3\times10^4$$  

• $$4\times10^2$$  

Multiple Choice

(8 x 10⁵⁵) ÷ (2 x 10⁵²)

• 6 x 10³

• 4 x 10³

• 4 x 10¹⁰⁷

• 4 x 10⁵⁵

Multiple Choice

Solve: $$\frac{(9\times10^{-6})}{(3\times10^{-3})}$$  

• $$27\times10^{-9}$$  

• $$3\times10^{-3}$$  

• $$3\times10^{-9}$$  

• $$27\times10^{-3}$$  

Multiple Choice

$$\frac{(6.9\times10^7)}{\left(2.3\times10^{-3}\right)}$$  

Divide: (6.9 x 107) / (2.3 x 10-3)

• $$3\times10^{10}$$  

• $$3\times10^4$$  

• $$3\times10^{-4}$$  

• $$4.6\times10^{10}$$  

Multiple Choice

Find the quotient. Write your answer in proper scientific notation.

2 x 10⁸ ÷ 8 x 10⁴

• 0.25 x 10⁴

• 4 x 10⁴

• 2.5 x 10³

• 2.5 x 10²

Multiple Choice

What is $$\sqrt[]{144}$$  ?

• 144

• 144

• 12

• 288

Multiple Choice

What is $$\sqrt[]{64}$$  ?

• 64

• 8

• 32

• 128

Multiple Choice

What is $$\sqrt[]{4}$$  ?

• 2

• 4

• 8

• 16

Multiple Choice

What is $$\sqrt[]{36}$$  ?

• 36

• 6

• 18

• 72

Multiple Choice

What is $$\sqrt[]{100}$$  ?

• 10

• 100

• 200

• 1

Multiple Choice

A perfect square is a number whose square root is ___________.

• even

• a never-ending

  (non-terminating) decimal

• rational

• odd

Multiple Choice

To find the square root of a number, you must divide it by 2.

• True

• False

Multiple Choice

The √20 is between which two consecutive integers?

• 2 & 3

• 3 & 4

• 4 & 5

• 5 & 6

Multiple Choice

Between which two consecutive whole numbers is the√200? 

• 13 and 14

• 15 and 16

• 14 and 15

• 11 and 12

Multiple Choice

x² = 121
What does x equal?

• 11²

• 11 and -11

• 20 and 11

• 12 and 1

Multiple Choice

Which number has a square root that is between 7 and 8?

• 48

• 81

• 60

• 36

Multiple Choice

The number 500...

• is a perfect square.

• is not a perfect square.

Multiple Choice

17² =

• 34

• 289

• 225

• 324

Multiple Choice

List in order from least to greatest.
5/4, 56%, 1.07, 4/5

• ^{5/4, 56%, 1.07, 4/5}

• ^{1.07, 4/5, 5/4, 56%}

• ^{56%, 1.07, 4/5, 5/4}

• ^{56%, 4/5, 1.07, 5/4}

Multiple Choice

Which list of numbers is in order from least to greatest?

• A √23, 5, 6, 43%

• B 5, √23, 6, 43%

• C 43%, 5, √23, 6

• D 43%, √23, 5, 6

Multiple Choice

Order from least to greatest:
6.9, √37, √25, 28/4

• 6.9, √37, √25, 28/4

• 28/4, 6.9, √37, √25, 

• √37, √25, 28/4, 6.9

• √25, √37, 6.9, 28/4

Multiple Choice

Order from greatest to least:
14/5, √5,  √4, 1.8

• 14/5, √5, √4, 1.8

• √4, √5, 14/5, 1.8

• 14/5, √5,  √4, 1.8

• 1.8, √4, √5, 14/5

Rational

Values that can be written as a fraction.

Look for: fractions, whole numbers, terminating decimals, repeating decimals, and perfect squares.

Irrational

Values that can NOT be written as a fraction.

Look for: Never-ending non-repeating decimals, pi, and imperfect squares.

Multiple Choice

Categorize the following:  $$\frac{3}{4}$$   

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$-32$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$5.984732...$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$7.\overline{5}$$  

• Rational

• Irrational

Multiple Choice

Categorize the following:  $$-2.3$$  

• Rational

• Irrational

Multiple Choice

Categorize the following: $$\sqrt{36}$$  

• Rational

• Irrational

Multiple Choice

Categorize the following: $$\sqrt{15}$$  

• Rational

• Irrational

Multiple Choice

Classify the following: $$\sqrt{64}$$  

• Rational

• Irrational 

• Neither 

• Both 

Multiple Choice

Classify the following: $$\frac{3}{4}$$  

• Rational

• Irrational

• Neither

• Both 

Multiple Choice

Is the following rational? $$\sqrt{2}$$  

• Yes 

• No

• Sometimes

• Um... 

Multiple Choice

Classify the following: $$-17$$  

• Rational 

• Irrational

• Neither

• Both 

Multiple Choice

Is the following irrational? $$-96.\overline{33}$$  

• Yes

• No

• Sometimes

• I wanna say "Larry"...

Multiple Choice

Classify the following: $$\pi$$  

• Rational 

• Irrational 

• Neither

• Both 

Multiple Choice

Classify the following: $$0.525$$  

• Rational 

• Irrational 

• Neither

• Both 

Multiple Choice

Which of the following numbers is not rational?

• $$-3$$

• $$2.7$$

• $$\sqrt{4}$$

• $$\sqrt{5}$$

Multiple Choice

Which of the following number is rational?

• $$\sqrt{127}$$

• $$\pi$$

• $$2.5$$

• $$8.98763...$$

Multiple Choice

Which of the following is an irrational number?

• $$\sqrt{0}$$

• $$\sqrt{3}$$

• $$1\overline{.36}$$

• $$-0.19$$