1- 28000000000 mg into Oz(scientific notation). 2- 3600 km/hr into meter/second(m/s) (scientific notation). 3- 6000 KL into cm³ (scientific notation). 4- 508000000000nm into Inch (scientific notation). 5- -31 °F into °K. 6- 103 °K into °F. 7- Write the following number in standard scientific notation: 0.000000302 x 10 (scientific notation)
The Correct Answer and Explanation is:
Here are the solutions for your conversion and scientific notation questions:
1. 28000000000 mg into Oz (scientific notation)
To convert milligrams (mg) to ounces (oz), we use the conversion factor:
1 oz = 28,349.5 mg. 28000000000 mg×(1 oz28349.5 mg)=987.0 oz28000000000 \, \text{mg} \times \left( \frac{1 \, \text{oz}}{28349.5 \, \text{mg}} \right) = 987.0 \, \text{oz}28000000000mg×(28349.5mg1oz)=987.0oz
Now, in scientific notation: 987.0=9.87×102 oz.987.0 = 9.87 \times 10^2 \, \text{oz}.987.0=9.87×102oz.
So, 28000000000 mg = 9.87 x 10² oz.
2. 3600 km/hr into m/s (scientific notation)
To convert kilometers per hour (km/h) to meters per second (m/s), use the following conversion factors: 1 km=1000 mand1 hr=3600 s.1 \, \text{km} = 1000 \, \text{m} \quad \text{and} \quad 1 \, \text{hr} = 3600 \, \text{s}.1km=1000mand1hr=3600s.
So, 3600 km/h×(1000 m1 km)×(1 hr3600 s)=1000 m/s.3600 \, \text{km/h} \times \left( \frac{1000 \, \text{m}}{1 \, \text{km}} \right) \times \left( \frac{1 \, \text{hr}}{3600 \, \text{s}} \right) = 1000 \, \text{m/s}.3600km/h×(1km1000m)×(3600s1hr)=1000m/s.
In scientific notation, this is: 1000=1.0×103 m/s.1000 = 1.0 \times 10^3 \, \text{m/s}.1000=1.0×103m/s.
So, 3600 km/hr = 1.0 x 10³ m/s.
3. 6000 KL into cm³ (scientific notation)
To convert kiloliters (KL) to cubic centimeters (cm³), use: 1 KL=1,000,000 cm3.1 \, \text{KL} = 1,000,000 \, \text{cm}^3.1KL=1,000,000cm3.
So, 6000 KL=6000×1,000,000=6×109 cm3.6000 \, \text{KL} = 6000 \times 1,000,000 = 6 \times 10^9 \, \text{cm}^3.6000KL=6000×1,000,000=6×109cm3.
Therefore, 6000 KL = 6.0 x 10⁹ cm³.
4. 508000000000 nm into Inches (scientific notation)
To convert nanometers (nm) to inches, use: 1 inch=25.4×106 nm.1 \, \text{inch} = 25.4 \times 10^6 \, \text{nm}.1inch=25.4×106nm.
So, 508000000000 nm×(1 inch25.4×106 nm)=20,000 inches.508000000000 \, \text{nm} \times \left( \frac{1 \, \text{inch}}{25.4 \times 10^6 \, \text{nm}} \right) = 20,000 \, \text{inches}.508000000000nm×(25.4×106nm1inch)=20,000inches.
In scientific notation: 20000=2.0×104 inches.20000 = 2.0 \times 10^4 \, \text{inches}.20000=2.0×104inches.
Thus, 508000000000 nm = 2.0 x 10⁴ inches.
5. -31 °F into Kelvin (°K)
To convert Fahrenheit (°F) to Kelvin (°K), use the formula: K=59×(°F−32)+273.15.K = \frac{5}{9} \times (°F – 32) + 273.15.K=95×(°F−32)+273.15.
Substitute -31 °F into the equation: K=59×(−31−32)+273.15=59×(−63)+273.15=−35+273.15=238.15 K.K = \frac{5}{9} \times (-31 – 32) + 273.15 = \frac{5}{9} \times (-63) + 273.15 = -35 + 273.15 = 238.15 \, \text{K}.K=95×(−31−32)+273.15=95×(−63)+273.15=−35+273.15=238.15K.
So, -31 °F = 238.15 K.
6. 103 °K into Fahrenheit (°F)
To convert Kelvin (°K) to Fahrenheit (°F), use the formula: °F=95×(K−273)+32.°F = \frac{9}{5} \times (K – 273) + 32.°F=59×(K−273)+32.
Substitute 103 K into the equation: °F=95×(103−273)+32=95×(−170)+32=−306+32=−274 °F.°F = \frac{9}{5} \times (103 – 273) + 32 = \frac{9}{5} \times (-170) + 32 = -306 + 32 = -274 \, \text{°F}.°F=59×(103−273)+32=59×(−170)+32=−306+32=−274°F.
Therefore, 103 °K = -274 °F.
7. Write the number 0.000000302 × 10 in standard scientific notation:
To convert 0.000000302×100.000000302 \times 100.000000302×10 into standard scientific notation:
- Shift the decimal point in 0.000000302 7 places to the right, so we get 3.023.023.02.
- Adjust the exponent to account for the shift in decimal places.
Thus, 0.000000302×10=3.02×10−70.000000302 \times 10 = 3.02 \times 10^{-7}0.000000302×10=3.02×10−7.
So, 0.000000302 x 10 = 3.02 x 10⁻⁷ in scientific notation.
