Convert 80 km/h to m/s (using scientific notation and also express your answer in scientific notation). * The density of a substance is 19.6 g/mL, convert this to kg/L (using scientific notation and also express your answer in scientific notation)
The Correct Answer and Explanation is:
Conversion 1: 80 km/h to m/s
To convert kilometers per hour (km/h) to meters per second (m/s), multiply by 10003600\frac{1000}{3600}36001000 because:
- 1 kilometer = 1000 meters
- 1 hour = 3600 seconds
80×10003600=800003600≈22.2222 m/s80 \times \frac{1000}{3600} = \frac{80000}{3600} \approx 22.2222 \text{ m/s}80×36001000=360080000≈22.2222 m/s
Expressed in scientific notation:22.2222 m/s≈2.22×101 m/s22.2222 \text{ m/s} \approx 2.22 \times 10^1 \text{ m/s}22.2222 m/s≈2.22×101 m/s
Conversion 2: 19.6 g/mL to kg/L
Start by recognizing the relationships:
- 1 gram = 0.001 kilograms
- 1 milliliter = 0.001 liters
This means that:19.6 g/mL=19.6×(0.001 kg1 g)÷(0.001 L1 mL)19.6 \text{ g/mL} = 19.6 \times \left(\frac{0.001 \text{ kg}}{1 \text{ g}}\right) \div \left(\frac{0.001 \text{ L}}{1 \text{ mL}}\right)19.6 g/mL=19.6×(1 g0.001 kg)÷(1 mL0.001 L)=19.6 kg/L= 19.6 \text{ kg/L}=19.6 kg/L
In scientific notation:19.6 kg/L=1.96×101 kg/L19.6 \text{ kg/L} = 1.96 \times 10^1 \text{ kg/L}19.6 kg/L=1.96×101 kg/L
Explanation (300 words)
Unit conversions rely on understanding how units relate to one another. Converting 80 km/h to m/s involves recognizing that a kilometer consists of 1000 meters and an hour has 3600 seconds. Multiplying 80 by the fraction 10003600\frac{1000}{3600}36001000 simplifies to dividing by 3.6, which results in approximately 22.2222 m/s. This value is then rewritten in scientific notation as 2.22×101 m/s2.22 \times 10^1 \text{ m/s}2.22×101 m/s, a common format used to represent large or small numbers efficiently.
For density, the conversion of 19.6 g/mL to kg/L is more direct. One gram is a thousandth of a kilogram, and one milliliter is a thousandth of a liter. These thousandths cancel each other out when both numerator and denominator are converted, meaning the numerical value remains unchanged. Therefore, 19.6 g/mL equals 19.6 kg/L. However, expressing this in scientific notation enhances clarity in scientific contexts. The number 19.6 becomes 1.96×1011.96 \times 10^11.96×101.
These conversions illustrate a critical principle in science and engineering: the ability to work with units and express values precisely using scientific notation. This helps in ensuring consistent calculations, reducing errors, and improving readability, particularly in academic, laboratory, and technical environments.
