In the Real World Examples

Find (5.4 × 10⁷) + (3.23 × 10⁹).

There are two ways to do this.

Way 1: Since 5.4 × 10⁷ = 0.054 × 10⁹, we can rewrite the original problem as:

(0.054 × 10⁹) + (3.23 × 10⁹)

Then we just add the decimals to get 3.284 × 10⁹.

Way 2: Since 3.23 × 10⁹ = 323 × 10⁷, we can rewrite the original problem as:

(5.4 × 10⁷) + (323 × 10⁷)

This simplifies to 328.4 × 10⁷, which in scientific notation is 3.284 × 10⁹.

Find (3 × 10⁴)(5 × 10²). Write the answer in scientific notation.

Since multiplication can be done in any order, we can rewrite this as (3 × 5)(10⁴ × 10²). It makes our lives easier that multiplication has the versatility of Tom Hanks. We can then simplify to 15 × 10⁶, which in scientific notation is 1.5 × 10⁷. Houston, we don't have a problem. Aw yeah.