Operations of-scientific-notation (Kyle Balais)

Physical Science

1. Operations of scientific notation Rules O perations Power of 10 exponent

2. Scientific notation makes it easier to read, write, and calculate with very large and very small numbers . You can add, subtract, multiply, and divide numbers that are written in scientific notation while still keeping the numbers in scientific notation.

3. The  coefficient  must be greater than 1 and less than 10 and contain all the significant (non-zero) digits in the number 12.5 × 10 6  is not in proper scientific notation, since the coefficient is greater than 10 . Neither is 0.125 × 10 7 , since the coefficient is less than 1 .

4. The  base  is always 10. The  exponent  is the number of places the decimal was moved to obtain the coefficient.

5. When adding or subtracting numbers in scientific notation, where the exponents must be the same . Step 1 - add/subtract the decimal Step 2 – Bring down the given exponent on the 10

6. Example 1 ( 2.56 X 10 3 ) + ( 6.964 X 10 3 ) Step 1 - Add: 2.56 + 6.964 = 9.524 Step 2 – Bring down exponent : 9.524 x 10 3

7. Try this: The sum of 5.6 x 10 3 and 2.4 x 10 3 is: A 8.0 x 10 3 B 8.0 x 10 6 C 8.0 x 10 -3 D 8.53 x 10 3 4.86 x 10 3 – 4.72 x 10 3 Subtract this : Answer: = 1.4 x 10 2

8. Adding/Subtracting when the Exponents are DIFFERENT When adding or subtracting numbers in scientific notation, the exponents must be the same. If they are different, you must move the decimal so that they will have the same exponent.

9. It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10. Moving the Decimal Step 1 – Rewrite so the exponents are the same Step 2 - add/subtract the decimal Step 3 – Bring down the given exponent on the 10

10. Adding With Different Exponents (4.12 x 10 6 ) + (3.94 x 10 4 ) (412 x 10 4 ) + (3.94 x 10 4 ) 412 + 3.94 = 415.94 415.94 x 10 4 Express in proper form: 4.15 x 10 6 Subtracting With Different Exponents (4.23 x 10 3 ) – (9.56 x 10 2 ) (42.3 x 10 2 ) – (9.56 x 10 2 ) 42.3 – 9.56 = 32.74 32.74 x 10 2 Express in proper form: 3.27 x 10 3

11. A B C D 7.8 x 10 5 minus 3.5 x 10 4 is 7.45 x 10 5 4.3 x 10 4 4.3 x 10 6 4.3 x 10 10 3.6 x 10 5 + 2.7 x 10 4 Add this: = 3.87 x 10 5

12. Adding and Subtracting… The important thing to remember about adding or subtracting is that the exponents must be the same! If the exponents are not the same then it is necessary to change one of the numbers so that both numbers have the same exponential value .

13. (3.45 x 10 3 ) + (6.11 x 10 3 ) (4.12 x 10 6 ) + (3.94 x 10 4 ) (8.96 x 10 7 ) – (3.41 x 10 7 ) ( 2.9785 x 10 -8 ) – (5.72x 10 -10 )