Test on Numbers

Thursday 7th OctoberSurds

Index lawsCubes and SquaresScientific Notation

Quick Revisit- Surds

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72

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144

€

200€

6 212

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10 2

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2 25 10

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4 200

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40 2

Quick check Index Laws

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a7

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b3

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a6

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3b4

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3

Order each set of numbers from least to greatest ( ascending order)

Order each set of numbers from least to greatest ( ascending order)- solutions

POWERS of 10

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101 =10

102 =10 ×10 =100

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102 =10 ×10 =100

103 =

104 =

105 =

106 =

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10 ×10 ×10 =1000

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10 ×10 ×10 ×10 =10000

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10 ×10 ×10 ×10 ×10 =100000

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10 ×10 ×10 ×10 ×10 ×10 =1000000

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102 =10 ×10 =100

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200 = 2 ×100 = 2 ×102

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100 =10 ×10 =102

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2000

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=2

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=2 ×10 ×10 ×10

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=

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2 ×103

Write 6 million as power of 10

Write 20000 as power of 10

Write 15000 as power of 10€

=6000000 = 6 ×106

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=2 ×104

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=15 ×103

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=1.5 ×10 ×103

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=1.5 ×104

An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms.

The average size of an atom is about 0.00000003 centimeters across.

The length of these numbers in standard notation makes them awkward to work with.

Scientific notation is a shorthand way of writing such numbers.

The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

Helpful Hint

In scientific notation the number of atoms in a penny is 2.0 1022,

and the size of each atom is 3.0 10–8 centimeters across.

An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms.

The average size of an atom is about 0.00000003 centimeters across.

Translating Standard Notation to Scientific Notation

Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative.

0.00709 Move the decimal to get a number between 1 and 10.7.09

7.09 10 Set up scientific notation.

Think: The decimal needs to move 3 places.

Check 7.09 10–3 = 7.09 0.001 = 0.00709

Write 0.00709 in scientific notation.

So 0.00709 written in scientific notation is 7.09 10–3.

Try This: Example 2

Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative.

0.000811 Move the decimal to get a number between 1 and 10.

8.11

8.11 10 Set up scientific notation.

Think: The decimal needs to move 4 places.

Check 8.11 10 = 8.11 0.0001 = 0.000811–4

Write 0.000811 in scientific notation.

So 0.000811 written in scientific notation is 8.11 10–4.

A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to end, how many millimeters long would they be? Write the answer in scientific notation.

187 mm 10,000

1 centimeter = 10 millimeters, so 18.7 centimeters = 187 millimeters

Find the total length.

1,870,000 mm

Additional Example 3: Application

Think: The decimal needs to move 6 places.

The 10,000 pencils would be 1.87 106 mm long, laid end to end. This is about one mile long.

Additional Example 3 Continued

1.87 10 Set up scientific notation.Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive.

1,870,000 mm

An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation.

2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable

Each cable can hold 300,000 pounds.

Try This: Example 3

Find the weight each cable is expected to hold by dividing the total weight by the number of cables.

Now write 300,000 pounds in scientific notation.

Think: The decimal needs to move right to change 3.0 to 300,000, so the exponent will be positive.

Think: The decimal needs to move 5 places.

Each cable can hold 3.0 10 pounds.5

3.0 10 Set up scientific notation.

Try This: Example 3 Continued

Multiplying and Dividing numbers in Scientific Notation form

What is the product of:

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2.15 ×103 And

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3.0 ×108

(use index laws) and express answer in SN

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2.15 ×103

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3.0 ×108X

Same base, different exponent or index

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2.15 × 3.0 ×103 ×108

If same base number, add the index

Write them out so that same base numbers are next to each other

Multiply the whole numbers

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2.15 × 3.0 ×1011

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6.45 ×1011

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6.45 ×1011 ÷ 3.15 ×106

Dividing numbers in SN form

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6.45 ×1011

3.15 ×1061. Rewrite it as one over the other

2. Use index laws: if dividing same base numbers, subtract the indices

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6.45 ×1011−6

3.15

3. Complete operation with index numbers

4. Divide whole numbers

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6.45 ×105

3.15

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2.05 ×105

Lesson Quiz

Write in standard notation.

1. 1.72 104

2. 6.9 10–3

4. 57,000,000

17,200

0.0069

3. 0.0053 5.3 10–3

5.7 107

Write in scientific notation.

5. A human body contains about 5.6 x 106 microliters of blood. Write this number in standard notation.

5,600,000

6. Evaluate and express in SN

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8 ×1012 ÷ 2 ×106

7. Evaluate and express in SN

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3×1017 × 2.3×103

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4 ×106

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6.9 ×1020

135,000

1.35 100,000

Think: Move the decimal right 5 places.

A. 1.35 105

1.35 10 5 10 = 100,0005

Additional Example 1A: Translating Scientific Notation to Standard Notation

Write the number in standard notation.

2,870,000,000

2.87 1,000,000,000

Think: Move the decimal right 9 places.

A. 2.87 109

2.87 10 9 10 = 1,000,000,0009

Write the number in standard notation.

Try This: Example 1A

0.0027

Divide by the reciprocal.2.7 100

Think: Move the decimal left 3 places.

2.7 10 –3

B. 2.7 10 –3

10 = –3 1100

2.7 1

100

Write the number in standard notation.

Additional Example 1B: Translating Scientific Notation to Standard Notation Continued

C. –2.01 104

–20,100 Think: Move the decimal right 4 places.

–2.01 10 4

10 = 10,0004

–2.01 10,000

Additional Example 1C: Translating Scientific Notation to Standard Notation Continued

Write the number in standard notation.

1.9 10,000

0.000019

Divide by the reciprocal.

Think: Move the decimal left 5 places.

1.9 10 –5

B. 1.9 10–5

–5 110 =

10,000

Write the number in standard notation.

1.9 1

10,000

Try This

10 = 100,000,0008–5.09 10 8

–5.09 100,000,000

C. –5.09 108

Write the number in standard notation.

Try This

–509,000,000 Think: Move the decimal right 8 places.

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

1. 14.28 x 10-4

2. 1.428 x 10-3

3. 14.28 x 1010

4. 1.428 x 1011

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108