Scientific Notation Practice

Writing a Number in Scientific Notation:

1. Move the decimal point to the right of the first nonzero digit
2. Count the number of places the decimal point was moved
   • This will be the absolute value of the exponent on 10
3. The exponent on 10 will be positive if the original number is greater than the number in step 1
4. The exponent on 10 will be negative if the original number is less than the number in step 1
5. If the decimal point was not moved in step 1, the exponent on 10 is 0

Converting from Scientific Notation to Standard Form:

1. Use the exponent on 10 to decide how many places to move the decimal point in the decimal number
2. If the exponent is positive, move the decimal point to the right
3. If the exponent is negative, move the decimal point to the left
4. After adjusting the decimal point, remove the × 10ⁿ part

Multiplying and Dividing with Scientific Notation:

1. Group the decimal numbers together
2. Group the powers of 10 together
3. Multiply or divide the decimal numbers
4. Use the rules of exponents to multiply or divide the powers of 10
5. Rewrite the result in scientific notation

Adding and Subtracting with Scientific Notation:

1. Make sure both numbers have the same exponent on 10
   • If they don't change one of the numbers so that the exponents on 10 match
2. Factor out the common power of 10 using the distributive property:
   • (a × 10ⁿ) + (b × 10ⁿ) = (a + b) × 10ⁿ
3. Add or subtract the decimal numbers
4. Rewrite the result in scientific notation

Step-by-Step: