OPERATIONS IN SCIENTIFIC NOTATION

Performing scientific surgery…

2 TYPES

• Multiplication and Division

(2 × 102)(3 × 10-6) = ?

• Addition and Subtraction

(2 × 102) + (3 × 10-6) = ?

Multiplication and Division

1. Multiply (divide) the “numerical” parts of the numbers, leaving the powers of ten out of the calculation for now:

(2) (3) = 6∙

2. Add (subtract) the powers of them if you are multiplying (dividing) those numbers:

(10+2) (10∙ -6) = 10(+2-6) = 10-4

3. Put it all together. Write the answer in proper scientific notation if necessary:

(2 × 102)(3 × 10-6) = 6 × 10-4

4. Answer: 6 × 10-4.

CAUTION!

YOU MUST… … STILL CHECK FOR SIGNIFICANT

FIGURES,AND

PUT THE FINAL ANSWER IN PROPER SCIENTIFIC NOTATION!

Addition and Subtraction 1. Rewrite all terms in the same power of ten

(yes, this means writing at least one of them in improper scientific notation):

(2 × 102) + (3 × 10-6) = (200000000 × 10-6) + (3 × 10-6) 2 + 6 = 8 decimal places

2. Perform the operation:(200000000 × 10-6) + (3 × 10-6) = 200000003 × 10-6

3. Put the answer in proper scientific notation:Answer: 2.00000003 × 102

THE END

Lilian Wehner ©