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Scientific Notation

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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

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:

- 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.

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.

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

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

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 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

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

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!