Adding and Subtracting Numbers in Scientific Notation

1. Adding and Subtracting Numbers in Scientific Notation Created by: Langan, Kansky, Nizam, O’Donnell, and Matos

2. Using Scientific Notation in Multiplication, Division, Addition and Subtraction Scientists must be able to use very large and very small numbers in mathematical calculations. As a student in this class, you will have to be able to multiply, divide, add and subtract numbers that are written in scientific notation. Here are the rules.

3. When adding or subtracting numbers in scientific notation, the exponents must be the same.

4. Adding/Subtracting when Exponents are THE SAME Step 1 - add/subtract the decimal Step 2 – Bring down the given exponent on the 10

5. Example 1 (2.56 X 103) + (6.964 X 103) Step 1 - Add: 2.56 + 6.964 = 9.524 Step 2 – Bring down exponent : 9.524x 103

6. Example 2 (9.49 X 105) – (4.863 X 105) Step 1 - Subtract: 9.49 – 4.863 = 4.627 Step 2 – Bring down exponent: 4.627x 105

7. The sum of 5.6 x 103 and 2.4 x 103 is A 8.0 x 103 B 8.0 x 106 C 8.0 x 10-3 D 8.53 x 103

8. The sum of 5.6 x 103 and 2.4 x 103 is A 8.0 x 103 B 8.0 x 106 C 8.0 x 10-3 D 8.53 x 103 The exponents are the same, so add the coefficients.

9. 8.0 x 103 minus 2.0 x 103 is A 6.0 x 10-3 B 6.0 x 100 C 6.0 x 103 D 7.8 x 103

10. 8.0 x 103 minus 2.0 x 103 is A 6.0 x 10-3 B 6.0 x 100 C 6.0 x 103 D 7.8 x 103

11. 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.

12. Moving the Decimal 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.

13. Adding/Subtracting when the Exponents are DIFFERENT 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

14. Adding With Different Exponents • (4.12 x 106) + (3.94 x 104) • (412 x 104) + (3.94 x 104) • 412 + 3.94 = 415.94 • 415.94 x 104 • Express in proper form: 4.15 x 106

15. Subtracting With Different Exponents • (4.23 x 103) – (9.56 x 102) • (42.3 x 102) – (9.56 x 102) • 42.3 – 9.56 = 32.74 • 32.74 x 102 • Express in proper form: 3.27 x 103

16. Example 3 (2.46 X 106)+ (3.4 X 103) Step 1 – Rewrite with the same exponents 3.4 X 103  0.0034 X 103+3 New Problem: (2.46 X 106)+ (0.0034 X 106) Step 2 – Add decimals 2.46 + 0.0034 = 2.4634 Step 3 – Bring Down Exponents 2.4634 X 106

17. Example 4 (5.762 X 103)– (2.65 X 10-1) Step 1 – Rewrite with the same exponents 2.65 X 10-1  0.000265 X 10(-1+4) New Problem : (5.762 X 103) – (0.000265 X 103) Step 2 – Subtract Decimals 5.762 – 0.000265 = 5.762 Step 3 – Bring down decimals 5.762X 103

18. 7.0 x 103 plus 2.0 x 102 is A 9.0 x 103 B 9.0 x 105 C 7.2 x 103 D 7.2 x 102

19. 7.0 x 103 plus 2.0 x 102 is A 9.0 x 103 B 9.0 x 105 C 7.2 x 103 D 7.2 x 102

20. 7.8 x 105 minus 3.5 x 104 is A 7.45 x 105 B 4.3 x 104 C 4.3 x 106 D 4.3 x 1010

21. 7.8 x 105 minus 3.5 x 105 is 7.45 x 105 A B 4.3 x 104 C 4.3 x 106 D 4.3 x 1010

22. 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.

23. Practice • (3.45 x 103) + (6.11 x 103) • (4.12 x 106) + (3.94 x 104) • (8.96 x 107) – (3.41 x 107) • (4.23 x 103) – (9.56 x 102)