Adding and Subtracting Numbers in Scientific Notation Using

Adding and Subtracting Numbers in Scientific Notation

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.

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

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

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. 524 x 103

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. 627 x 105

3 3 The sum of 5. 6 x 10 and 2. 4 x 10 is A B C D 8. 0 x 10 3 8. 0 x 10 6 -3 8. 53 x 10 3

3 3 The sum of 5. 6 x 10 and 2. 4 x 10 is A B C D 8. 0 x 10 3 8. 0 x 10 6 -3 8. 53 x 10 3 The exponents are the same, so add the coefficients.

3 3 8. 0 x 10 minus 2. 0 x 10 is A B C D 6. 0 x 10 -3 6. 0 x 10 0 6. 0 x 10 7. 8 x 10 3 3

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.

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.

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

Adding With Different Exponents • • (4. 12 x 106) + (3. 94 x 104) (412 x 104) + (3. 94 x 104) 412 + 3. 94 = 415. 94 x 104 • Express in proper form: 4. 15 x 106

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 x 102 • Express in proper form: 3. 27 x 103

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

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. 762 X 103

3 2 7. 0 x 10 plus 2. 0 x 10 is A B C D 9. 0 x 10 7. 2 x 10 3 5 3 2

5 4 7. 8 x 10 minus 3. 5 x 10 is A B C D 7. 45 x 10 4. 3 x 10 5 4 4. 3 x 10 6 10

5 5 7. 8 x 10 minus 3. 5 x 10 is A B C D 7. 45 x 10 4. 3 x 10 5 4 4. 3 x 10 6 10

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.

Practice 1) (3. 45 x 103) + (6. 11 x 103) 2) (4. 12 x 106) + (3. 94 x 104) 1) (8. 96 x 107) – (3. 41 x 107) 2) (4. 23 x 103) – (9. 56 x 102)