Finish these equations

7000 = 7 x 10n

600,000 = 6 x 10n

30,000,000 = 3 x 10n

3

5

7

1.47 x 100 =

82 x 10,000 =

0.0629 x 1000 =

147

820,000

62.9

Scientists use easy ways to write large numbers. This easy way is more compact & more useful.

This compact, useful method is called

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

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

Criteria:

a.One factor is a number GREATER than or EQUAL to 1, but LESS 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

4,064,000

25,000

714,500

156,000,000

1.2 x 105

4.064 x 106

2.5 x 104

7.145 x 105

1.56 x 108

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

Do the OPPOSITE. 1.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

9 x 105

1.9 x 104

7.005 x 107

9.415 x 108

90,700

900,000

19,000

70,050,000

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:

0.00064=

Follow these rules:

1.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.

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 =

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!

7.9 x 10-7

7.16 x 10-5

4.5 x 10-3