Question

1.) 4,58⋅10^5 л =_⋅10^_ м3; 2.) 54⋅10^4 км/ч =_⋅10^_ м/с; 3.) 3,2⋅10^8 м^2 =_⋅10^_ га.

Answer 1

1) 1 м³ = 1000 дм³ = 10³ л

$4,58 \cdot 10^5$ л = $4,58 \cdot 10^5 \cdot 10^{-3}$ м³ = $4,58 \cdot 10^2$ м³

2) 1 км/ч = $\frac{1000}{3600}$ м/с = $\frac{5}{18}$ м/с

$54 \cdot 10^4$ км/ч = $54 \cdot 10^4 \cdot \frac{5}{18}$ м/с = $1,5 \cdot 10^5$ м/с

3) 1 га = 10000 м² = $10^4$ м²

$3,2 \cdot 10^8$ м² = $3,2 \cdot 10^8 \cdot 10^{-4}$ га = $3,2 \cdot 10^4$ га

Answer 2

To convert the given quantities to different units, we'll use the principles of scientific notation. In scientific notation, a number is represented as "a × 10^b", where "a" is a coefficient between 1 and 10 (inclusive) and "b" is the exponent representing the power of 10.

1. To convert liters (л) to cubic meters (м^3):

Given: 4.58 × 10^5 л = _ × 10^_ м^3

Since 1 cubic meter (м^3) equals 1000 liters (л), we can use this conversion factor to perform the conversion:

4.58 × 10^5 л = (4.58 × 10^5) / 1000 м^3 = 4.58 × 10^2 м^3

So, 4.58 × 10^5 л = 4.58 × 10^2 м^3

2. To convert kilometers per hour (км/ч) to meters per second (м/с):

Given: 54 × 10^4 км/ч = _ × 10^_ м/с

To convert km/h to m/s, we divide by 3.6 since there are 3600 seconds in an hour (60 seconds/minute × 60 minutes/hour).

54 × 10^4 км/ч = (54 × 10^4) / 3.6 м/с ≈ 15 × 10^4 м/с = 15 × 10^4 м/с

So, 54 × 10^4 км/ч ≈ 15 × 10^4 м/с

3. To convert square meters (м^2) to hectares (га):

Given: 3.2 × 10^8 м^2 = _ × 10^_ га

Since 1 hectare (га) is equal to 10,000 square meters (м^2), we can use this conversion factor:

3.2 × 10^8 м^2 = (3.2 × 10^8) / 10,000 га = 32 × 10^4 га = 3.2 × 10^5 га

So, 3.2 × 10^8 м^2 = 3.2 × 10^5 га