Question

Perform the operations and answer in scientific and standard notation: (6 × 10^4) + (3 × 10^3)-

a) 9 × 10^4; 90,000.
b) 9 × 10^6; 9,000,000.
c) 9 × 10^3; 9,000.
d) 9 × 10^5; 900,000.

Answer 1

Option (a), To perform the addition, express both numbers with the same exponent. Adding (6 × 10^4) to (3 × 10^3), we get 6.3 × 10^4; in standard notation, it is 63,000.

Step-by-step explanation:

To add (6 × 10^4) and (3 × 10^3), you must first express them with the same exponent. Since 10^4 is the larger exponent, we'll convert (3 × 10^3) to an equivalent value with an exponent of 4:

(3 × 10^3) = (0.3 × 10^4)

Now, adding the two values:

(6 × 10^4) + (0.3 × 10^4) = (6 + 0.3) × 10^4

(6 + 0.3) is 6.3, so:

(6 + 0.3) × 10^4 = 6.3 × 10^4

To express 6.3 × 10^4 in standard notation and scientific notation correctly, we recognize that:

6.3 × 10^4 in scientific notation remains the same. In standard notation, you move the decimal four places to the right, giving:

63,000

The correct answer, in both scientific and standard notation, is:

a) 6.3 × 10^4; 63,000.