Scientific Notation

with positive powers of 10Lesson 2.2Mrs. Carley

Definition of Scientific Notation

• Scientific notation is a method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10 and a power of 10.

Scientific Notation

A number is expressed in scientific notation when it is in

the form

a x 10n

where a is between 1 and 9

and n is an integer

Example IWrite 4,776 in scientific notation

Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between

one and ten.

4.776Count the number of digits between the old and the new

decimal point, this gives the power, n of 10 (10n).

4 776 X 103

Since the decimal is shifted to the left, the exponent is positive.

4.776 x 103

3 Digits

Writing a number in Standard Notation

Example #2 Video

Example #2Write 4.953 x 104 in standard form

Write the decimal number.

4.953Move the decimal the number of places specified by the powers of ten: to the right since it is positive.

X 104 4 9530Rewrite the number in integer/standard form.

49,530

4 Places

Scientific notation with Negative Powers of 10

Lesson 2.3

Mrs. Carley

RULES• Writing numbers in Scientific Notation

– When I move the decimal to the right the exponent is negative.

– When I move the decimal to the left the exponent is positive.

• Writing numbers in Standard Notation– When I move the decimal to the right, the

number is positive– When I move the decimal to the left, the

number is negative.– HINT: Think about the number line

Example #1

• The average size of an atom is about 0.00000003 centimeters across. Write the average size of an atom in scientific notation.– Step 1: Place the decimal point– Step 2: Count the number of places you

moved the decimal point.– Step 3: Any time you move the decimal point

to the right….the exponent to the power of 10 is negative.

Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02The decimal was moved how many

places?8

When the original number is less than 1, the exponent is negative.

9.02 x 10-8

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108

Writing a Number in Standard Notation

Example #2

Example #2Platelets are one component of human blood. A typical platelet has a diameter of approximately 2.33 x 10-6 in standard notation.

– Step1: Use the exponent to the power of 10 to see how many places to move the decimal point.

– Step 2: Place the decimal point. Since you are going to write a number less than 2.33, move the decimal point to the left. Add place holder zeros if necessary.

Answer: 0.00000233

Another ExampleWrite 8.397 x 10-1 in standard form

Write the decimal number.

8.397Move the decimal the number of places specified by

the powers of ten: to the left since it is negative.

X 10-1 0 8 397Rewrite the number in integer/standard form.

0.8397

1 Place

Express 1.8 x 10-4 in decimal notation.0.00018

Express 4.58 x 106 in decimal notation.

4,580,000

Operations with Scientific Notation

Lesson 2.4

Mrs. Carley

Adding/Subtracting Numbers

• Look at Example#1:– Step1: Write each number in standard

notation– Step2: Complete the operation – add/ subtract– Step3: Write the answer in scientific notation

• Complete #1 “Your Turn” on page 52.

Multiplying Numbers in Scientific Notation

• Multiply: (5.1 * 104) x (2.3 * 106)1. Multiply the coefficients: 5.1 * 2.3 = 11.73

2. Add the powers of 10: 4+6 =10

3. Check to be sure the product is in scientific notation. (5.1 * 104) x (2.3 * 106) = 11.73 * 1010

• 1.173 * 1011

• Therefore, (5.1 * 104) x (2.3 * 106) = 1.173 * 1011

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

1. 14.28 x 10-4

2. 1.428 x 10-3

3. 14.28 x 1010

4. 1.428 x 1011

Dividing Numbers in Scientific Notation

• Divide (3.9 * 108)

(6.5 * 10-4)1. Divide the coefficients: 3.9 / 6.5 = 0.6

2. Subtract the powers of 10: 8 – (-4) = 12

3. Check to be sure the quotient is in scientific notation.

• (3.9 * 108) = 0.6 * 1012)

(6.5 * 10-4)

• 6.0 * 1011

Example #2 Page 52

• Complete #2-3 “your Turn”