5.1 Add and Subtract Large Number Scientific Notation Common Core Standards 8. EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. WARM-UP 1) Convert into standard or decimal form. 5.2 × 10 4 2) Convert into scientific notation. 604,000 Evaluate the expressions. 3) 604,000 + 52,000 4) 6.04 × 105 + 5.2 × 10 4 Add and Subtract Large Number Scientific Notation What are the rules for adding and subtracting scientific notation? (4 × 103 ) + (2 × 102 ) 4,000 + 200 = 4,200 = 4.2 × 103 NOTES The most straightforward way to add or subtract with scientific notation is to convert each back to its regular form. Examples Evaluate the expressions and write in scientific notation. (7.5 × 101) + (2 × 102 ) 3 2 (6.3 × 10 ) − (5 × 10 ) EXAMPLES A scientist found 2 asteroids with masses of 4.06 x 108 and 2 x 107 kilograms. Find the total mass and write your answer in scientific notation. EXAMPLES One elephant weighed 1.36 x 104 lbs and the other weighed 9 x 103 lbs. Find the difference in the total weights and write your answer in scientific notation. NOTES If the powers of ten are the same there is sometimes a shortcut: Just add or subtract the decimals and keep the power of ten. Examples Evaluate the expressions and write in scientific notation. (4.5 × 10 4 ) + (2 × 10 4 ) (7.3 × 105 ) − (5.1× 105 ) EXAMPLES A scientist found 2 asteroids with masses of 5.3 x 108 and 4 x 108 kilograms. Find the difference in their masses and write your answer in scientific notation. PRACTICE Evaluate the expressions and write in scientific notation. (8.4 × 105 ) − (7.1× 103 ) (9.16 × 103 ) + (2.5 × 10 4 ) EXAMPLES Evaluate the expressions and write in scientific notation. (9 × 105 ) − (7.4 × 105 ) FINAL QUESTION One elephant weighed 1.06 x 104 lbs and the other weighed 7.5 x 103 lbs. Find the total weight and write your answer in scientific notation.