Adding and Subtracting Adding and Subtracting Numbers in Scientific NotationNumbers in Scientific Notation

Adding and Subtracting Adding and Subtracting Numbers in Scientific NotationNumbers in Scientific Notation

Created by: Langan, Kansky, Nizam, O’Donnell, and Matos

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

The sum of 5.6 x 103 and 2.4 x 10

3 is

A 8.0 x 103

B 8.0 x 106

C 8.0 x 10-3

D 8.53 x 103

The sum of 5.6 x 103 and 2.4 x 10

3 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.

8.0 x 103 minus 2.0 x 10

3 is

A 6.0 x 10-3

B 6.0 x 100

C 6.0 x 103

D 7.8 x 103

8.0 x 103 minus 2.0 x 10

3 is

A 6.0 x 10-3

B 6.0 x 100

C 6.0 x 103

D 7.8 x 103

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 DecimalIt 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

DIFFERENTStep 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

• 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

• 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 exponents3.4 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

7.0 x 103 plus 2.0 x 10

2 is

A 9.0 x 103

B 9.0 x 105

C 7.2 x 103

D 7.2 x 102

7.0 x 103 plus 2.0 x 10

2 is

A 9.0 x 103

B 9.0 x 105

C 7.2 x 103

D 7.2 x 102

7.8 x 105 minus 3.5 x 10

4 is

A 7.45 x 105

B 4.3 x 104

C 4.3 x 106

D 4.3 x 1010

7.8 x 105 minus 3.5 x 10

5 is

A

B 4.3 x 104

C 4.3 x 106

D 4.3 x 1010

7.45 x 105

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)