A rectangular section of wilderness will be set aside as a new wildlife refuge. It's dimensions are 6 × 10³ meters by 3 × 10⁴ meters. Find the area of the land in square meters. Put you answer in scientific notation.

Question

A. 18 × 10⁷
B. 9.0 × 10⁹
C. 90 × 10⁸
D. 1.8 × 10⁸

Answer 1

To find the area of the land, we can multiply the length and width of the rectangular section of wilderness:

Area = (6 × 10³ meters) × (3 × 10⁴ meters)
= 6 × 3 × 10³ × 10⁴ meters²
= 18 × 10⁷ meters²

Therefore, the area of the land in square meters is 18 × 10⁷, which is equivalent to 1.8 × 10⁸.

The correct answer is D. 1.8 × 10⁸.

Answer 2

Multiply the expression on the left and match them with their appropriate result.
(6.77 × 10^-12) • (1.12 × 10^-6)=
(2 × 10^-3) • (3 × 10⁷)=
(9.1 × 10⁹) • (2.6 × 10²)=

(2.366 × 10¹²), (7.5824 × 10^-18), (6 × 10⁴)

Answer 3

To multiply numbers in scientific notation, you multiply the coefficients and add the exponents.

For the expression (6.77 × 10^-12) • (1.12 × 10^-6):

(6.77 × 1.12) = 7.5724
10^-12 • 10^-6 = 10^(-12+(-6)) = 10^-18

So, (6.77 × 10^-12) • (1.12 × 10^-6) = 7.5724 × 10^-18

For the expression (2 × 10^-3) • (3 × 10⁷):

(2 × 3) = 6
10^-3 • 10^7 = 10^(-3+7) = 10^4

So, (2 × 10^-3) • (3 × 10⁷) = 6 × 10^4

For the expression (9.1 × 10⁹) • (2.6 × 10²):

(9.1 × 2.6) = 23.66
10^9 • 10^2 = 10^(9+2) = 10^11

So, (9.1 × 10⁹) • (2.6 × 10²) = 23.66 × 10^11

Matching the expressions with their results:

(6.77 × 10^-12) • (1.12 × 10^-6) = 7.5724 × 10^-18 <--> (7.5824 × 10^-18)
(2 × 10^-3) • (3 × 10⁷) = 6 × 10^4 <--> (6 × 10⁴)
(9.1 × 10⁹) • (2.6 × 10²) = 23.66 × 10^11 <--> (2.366 × 10¹²)