Scientific Notation

Scientific Notation

Scientific Notation ---> Regular Notation

Regular Notation- The standard way, how we write normally numbers (ex: 280,000,000).

Scientific Notation- Shortened way to write a long number (ex: 2.8*10^8).

Comparing & Ordering Numbers in Scientific Notation

Step 1: Write everything in standard form.

Step 2: Compare or order the numbers.

Dividing Numbers in Scientific Notation

Step 1: Divide the numbers between 1 to 10 together.

Step 2: Subtract the second exponent from the first exponent.

Step 3: Make sure the final quotient is in scientific notation.

Reminder: Exponents do NOT need to be the same when dividing with scientific notation.

1. (4.25 * 10^6)/ (1.7 * 10^3)

= (4.25/1.7) * (10^6-3)

= 2.5 * 10^3

2. (3.6 * 10^7)/ (1.2 * 10^3)

= (3.6/1.2) * (10^7-3)

= 3 * 10^5

3. (8.08 * 10^-10)/ (4.0 * 10^-3)

= (8.08/4.0) * (10^-10--3)

= 2.02 * 10^-7

4. (5.25 * 10^8)/ (3.5 * 10^3)

= (5.25/3.5) * (10^8-3)

= 1.5 * 10^5

Multiplying Numbers in Scientific Notation

Step 1: Multiply the numbers between 1 and 10 together.

Step 2: Multiply the powers of 10 by adding the exponents.

Step 3: Make sure the final product is in scientific notation.

1. (3 * 10^4) (7.2 * 10^6)

=(3 * 7.2) (10^4 * 10^6)

= 2.16 * 10^11

2. (2.4 * 10^3) (1.5 * 10^5)

= (2.4 * 1.5) (10^3 * 10^5)

= 3.16 * 10^8

3. (5.2 * 10^-6) (1.1 * 10^-3)

= (5.2 * 1.1) (10^-6 * 10^-3)

= 5.72 * 10^-9

4. (6.8 * 10^4) (4.2 * 10^4)

= (6.8 * 4.2) (10^4 * 10^4)

= 2.856 * 10^9

Adding & Subtracting With Scientific Notation

• When adding or subtracting decimals in Standard Notation, it’s necessary to line the decimals up.

• When adding and subtracting decimals in Scientific Notation, it’s necessary for the exponents of the 10 to be the same.

When The Exponents Are Equal:

When The Exponents Are Not Equal: