A mining operation excavates 5.482x10^4 metric tonnes of ore each hour. In an 12 hour production shift, how much ore is excavated in kg, to 2 significant figures?
To convert metric tonnes to kilograms, you need to multiply by 1000 since there are 1000 kilograms in one metric tonne.
Given:
Excavation rate = 5.482 x 10^4 metric tonnes/hour
Shift duration = 12 hours
First, let's calculate the total amount of ore excavated in metric tonnes during the shift.
Total excavation = Excavation rate x Shift duration
Total excavation = 5.482 x 10^4 metric tonnes/hour x 12 hours
To multiply these values, we multiply the numerical coefficients and add the exponents:
Total excavation = (5.482) x (10^4) x (12)
Total excavation = 65.784 x 10^4
Next, let's convert the total excavation from metric tonnes to kilograms:
Total excavation in kg = Total excavation x 1000
Total excavation in kg = 65.784 x 10^4 x 1000
Again, multiply the numerical coefficient and add the exponents:
Total excavation in kg = 657.84 x 10^4
Finally, to express the answer with 2 significant figures, we round it to 2 digits:
Total excavation in kg ≈ 660 x 10^4 kg
In standard form, this can be written as:
Total excavation in kg ≈ 6.6 x 10^6 kg
To calculate the amount of ore excavated in kilograms during a 12-hour shift, you can use the following formula:
Amount of ore (in kilograms) = Amount of ore (in metric tonnes) × Conversion factor
Given that the mining operation excavates 5.482 × 10^4 metric tonnes per hour, we can calculate the amount of ore excavated in kilograms as follows:
Amount of ore (in metric tonnes) = 5.482 × 10^4 metric tonnes
Conversion factor: 1 metric tonne = 1000 kilograms
Now, let's work through the calculation:
Amount of ore (in kilograms) = 5.482 × 10^4 metric tonnes × 1000 kilograms/metric tonne
= 5.482 × 10^4 × 1000 kilograms (as 1 metric tonne = 1000 kg)
= 5.482 × 10^7 kilograms
To two significant figures, the answer is 5.5 × 10^7 kilograms.