Scientific Notation PowerPoint.ppt

Scientific

Notation

8th Grade Ch10

Outline

Objectives

•_{Use scientific notation to estimate very large or}

very small quantities.

• _{Perform operations with numbers expressed in}

scientific notation and other forms.

• _{Interpret scientific notation that has been}

generated by technology. Standards:

•_8.EE.3

•_8.EE.4

What is Scientific Notation

Identifying Scientific Notation

Two conditions must be met. Ask yourself:

•_{Is the factor between 1-10?}

•_{Does the power of 10 have an integer}

exponent?

Tell whether the number is written in scientific notation. Explain.

a. 2.5 × 10−9

yes; The factor is greater than or equal to 1 and less

than 10. The power of 10 has an integer exponent.

b. 0.5 × 106

no; The factor is less than 1.

Only one of these is in scientific notation. Can you tell which one?

Positive Exponents Make the # Bigger

• ₁₀1 = 10

• ₁₀2 = 10X10= 100

• ₁₀3 = 10X10X10 = 1000

• ₁₀4 = 10X10X10X10 = 10,000

Negative Exponents make the # Smaller

•

₁₀

= 1/10 = 0.1

•

₁₀

= 1/100 = 0.01

•

₁₀

= 1/1000 = 0.001

•

₁₀

= 1/10000 = 0.0001

Converting Between Standard Form & Scientific Notation

Standard Form Examples

• _{Positive exponent = move right} • _{Negative exponent – move left}

Warm Up

• _{Write each number in standard notation.}

1.2.54 x 102

2.6.7 x 102

3.1.14 x 103

• _{Write each number in scientific notation.}

4. 75,000,000

5.208

6. 907,100

Operations in

Scientific Notation

Add/Subtract

Add/Subtract with Scientific Notation

Examples with Same Power of Ten

Addition

•_{Given: (2.56 X 10}3 ) + (6.964 X 103)

•_{Add: 2.56 + 6.964 = 9.524} •_{Answer: 9.524 X 10}3

Subtraction

• _{Given: (9.49 X 10}5) – (4.863 X 105)

• _{Subtract: 9.49 – 4.863 = 4.627} • _{Answer: 4.627 X 10}5

Adjusting Powers

To add/subtract your powers must be the same.

To adjust your powers remember the acronym LARS

Moving the decimal left will add to the exponent. Moving the decimal right will subtract from the exponent.

Since adding to the exponent will make it larger and subtracting will make it smaller, you can also

remember:

22

Left – Larger

w

Adjusting Powers (things to remember)

• Remember when you add/subtract your powers of 10 must be the same.

• Generally it is best to change all the numbers in

scientific notation to the power of 10 with the HIGHEST exponent. This eliminates the extra step of putting the final answer back to proper scientific notation.

• When you increase the exponent the decimal decreases (or moves left). When you decrease the exponent the decimal increases (or moves right).

• So it might be more handy to remember:

Larger moves the decimal left. Smaller moves the decimal right.

Adjusting Powers (examples)

Larger = Left Smaller = Right.

Example 1) Adjust 3.603 x 102 to a power of 5

Since you need to make the exponent bigger by 3 move the decimal 3 places left

0.003603 x 102+3

= 0.003603 x 105

Example 2) Adjust 4.59 x 10-7 to have a power of -5

Since you need to make the exponent bigger by 2 move the decimal 2 places left

0.0459 x 10-7+2

0.0459 x 10-7

Adjusting Powers (examples continued)

Larger = Left Smaller = Right.

Example 3) Adjust 0.0831 x 104 to proper scientific notation

Since you need to move the decimal 2 places right make the exponent smaller

008.31 x 104-2

= 8.31 x 102

Example 4) Adjust 0.0052 x 10-1 _{to proper scientific notation}

Since you need to move the decimal 3 places right make the exponent smaller

005.2 x 10-1-3

5.2 x 10-4

28

Example – Add different exponents

• _{Given: (2.46 X 10}6 ) + (3.476 X 103 )

• _{You need to have the same power of 10. Lets}

change to 2nd one, so we need it to be 106

• _{Shift decimal 3 places to the left to get} 106.

• _{Move: .003476 X 10}3+3

• _{Add: (2.46 X 10}6 ) + (.003476 X 106)

• _{Answer: 2.463476 X 10}6

Note – It doesn’t matter which # you

move the decimal on, so long as they

both end with the same power of 10.

Left adds positive exponents

Example – Subtract Different Exponents

• _{Given: (7 X 10}5) – (5.2 X 104)

• _{Shift decimal 1 places to the right} for 105.

• _{Move: 70 X 10}[5+(-1)]

• _{Subtract: (70 X 10}4) – (5.2 X 104)

• _{Simplify: 64.8 x 10}4

• _{Answer: 6.48 X 10}5

Right adds negative exponents

Adjust to scientific

notation. Decimal moved left to a positive exponent was added

Your Turn

1. (5.30 x 103) + (0.60 x 103)

2. (7.5 x 103) + (5.25 x 105)

Answers

1. 5.90 x 103

2. ff

Operations in

Scientific Notation

Multiply/Divide

Multiplying with Scientific

Notation

1. Multiply the coefficients

2. Add the Exponents on the powers of ten.

3. Combine the answers

• ₁₀2 X 103 = 105

• _{100 X 1000 = 100,000}

Multiplying Example

(2.3 X 102)(3.3 X 103)

What it really means 230 X 3300

1. Multiply the Coefficients

• _{2.3 X 3.3 = 7.59}

2. Add the Exponents

• ₁₀2 X 103 = 105

3. Combine the answers

• _{7.59 X 10}5

Your Turn - Multiply

•

_{(4.6 X 10}

) X (5.5 X 10

) = ?

•

_{(3.1 X 10}

) X (4.2 X 10

) = ?

Dividing with Scientific Notation

Example - Dividing

(3.3 X 104)/ (2.3 X 102)

What this really means: 33000 / 230 = 143.4783

1. Divide the Coefficients

• _{3.3/ 2.3 = 1.434783}

2. Subtract the Exponents

• ₁₀4 / 102 = 102

3. Combine the answers:

• _{1.4347823 X 10}2

Your Turn - Divide

•

_{(4.6 X 10}

) / (5.5 X 10

) = ?

•

_{(3.1 X 10}

) / (4.2 X 10

) = ?

Answers 42

Note – Both answers need to

be adjusted to proper scientific