Scientific Notation
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Scientific Notation. Finish these equations. 7000 = 7 x 10 n. 3. 600,000 = 6 x 10 n. 5. 30,000,000 = 3 x 10 n. 7. 1.47 x 100 =. 147. 82 x 10,000 =. 820,000. 0.0629 x 1000 =. 62.9. Scientists use easy ways to write large numbers. This easy way is more compact & more useful.

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Scientific Notation

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Scientific notation

Scientific Notation


Scientific notation

Finish these equations

7000 = 7 x 10n

3

600,000 = 6 x 10n

5

30,000,000 = 3 x 10n

7

1.47 x 100 =

147

82 x 10,000 =

820,000

0.0629 x 1000 =

62.9


Scientific notation

Scientists use easy ways to write large numbers.

This easy way is more compact & more useful.

Scientific Notation

This compact, useful method is called

To write a number in Scientific Notation, express it as a product of two factors

There are 2 criteria for writing a number in Scientific Notation:


Scientific notation

  • Criteria:

  • One factor is a number GREATER than or EQUAL to 1, butLESS than 10. (This will usually be a decimal)

  • b. The other factor is a POSITIVE POWER of 10.

  • Let’s look at an example:

93,000,000

Notice that the decimal point is moved until it reaches a number greater than 1, but less than 10.


Scientific notation

How many times was the decimal point moved to the left? That answer is your exponent.

93,000,000 in Scientific Notation is: 9.3 x 107

Steps:

1. Move the decimal point to the LEFT until you get to a number greater than or equal to 1, but less than 10.

2. Count the number of places moved- that is the power of 10.


Scientific notation

Another example:

185,000

1.85 x 105

Let’s try some:

120,000

1.2 x 105

4,064,000

4.064 x 106

25,000

2.5 x 104

714,500

7.145 x 105

1.56 x 108

156,000,000


Scientific notation

How would you reverse Scientific Notation (write in standard form)?

  • Do the OPPOSITE.

  • Move the decimal point the number of places as the exponent in the Power of 10 to the RIGHT.

  • 2. Add 0’s as place fillers.

3.6 x 103

3,600


Scientific notation

Let’s try some

9.07 x 104

90,700

9 x 105

900,000

1.9 x 104

19,000

7.005 x 107

70,050,000

9.415 x 108

941,500,000


Scientific notation

Scientific Notation can also be used to rename large decimals that are between 0 & 1

These numbers will use negative exponents for their powers of 10.

Let’s look at an example:

  • Follow these rules:

  • First factor is greater than 1, but less than 10.

  • 2. Second factor is a power of 10 with a negative exponent. The exponent depends on how many times you moved the decimal to the RIGHT.

0.00064=

6.4 x 10-4


Scientific notation

Here’s another example:

0.0815 =

8.15 x 10-2

You try some:

0.015 =

0.0000086=

0.000124=

0.0069=

1.5 x 10-2

8.6 x 10-6

1.24 x 10-4

6.9 x 10-3


Scientific notation

0.00000079 =

0.0000716 =

0.0045 =

7.9 x 10-7

7.16 x 10-5

4.5 x 10-3

It is now your turn to explain how to write numbers in scientific notation. Explain the process of scientific notation to the person next to you. Explain it using whole numbers & decimal between 0 & 1. Pretend that your partner does not understand this process, so explain it well & with examples!


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