Scientific Notation

A number is expressed in scientific notation when it is written as the product of a number and a power of ten.The number must be greater than or equal to 1 and less than 10.

Number greater than or equal to 1, but less than 10

Power of 10 written in exponential form

The Distance From the Sun to the Earth

93,000,000

Step 1

Move decimal to the left Leave only ONE number in front of decimal

Step 2

Write number without zeros

Step 3

Count how many places you moved the decimal

Make that your exponent

Practice Problems

1) 98,500,000 = 9.85 x 10?

2) 64,100,000,000 = 6.41 x 10?

3) 279,000,000 = 2.79 x 10?

4) 420,000= 4.2 x 10?

Write in scientific notation. Decide the exponent.

9.85 x 107

6.41 x 1010

2.79 x 108

4.2 x 105

Standard form is the opposite of scientific notation

To write in standard form, move the decimal the same number of places as the exponent.

The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right.

More Practice Problems

1) 7.34 x 108

2) 8.7 x 103

3) 9 x 105

Write in standard form

1) 734,000,000 2) 8,700 3) 900,000

Let’s get started on the homework

W.S. 3-7 Front AND backRemember to be quiet!!

Warm-Up

Write in scientific notation1.) 2,000,000,0002.) 36,500,0003.) 465,000,000,000,000Write in standard form4.) 4.62 x 105

5.) 3 x 103

What if your number is a decimal?

Step 1:

Move decimal to the right Leave only one number in front of

decimal

Step 2

Write number without zeros

Step 3

Count how many places you moved the decimal

Make that your exponent Since your number was a decimal to begin

with the power is a negative!

Practice Problems

1) 0.00000658 = 6.58 x 10?

2) 0.000000000641 = 6.41 x 10?

3) 0.0000000123 = 1.23 x 10?

4) 0.0000068 = 6.8 x 10?

Write in scientific notation. Decide the power of ten.

6.58 x 10-6

6.41 x 10-10

1.23 x 10-8

6.8 x 10-6

Standard form is the opposite of scientific notation

To write in standard form, move the decimal the same number of places as the exponent.

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.

More Practice Problems

1) 4.35 x 10-8

2) 8.7 x 10-6

3) 5.2 x 10-5

Write in standard form

1) 0.0000000435 2) 0.0000087 3) 0.000052