Practice exercise 1
1. Convert the following masses into kilograms.
a) 58 475 μg
b) 406 dg
c) 1 900 cg
d) 945 Dg
e) 1 854 mg
f) 23 tonnes
Answer (1)
Convert micrograms to kilograms: 58475 μ g = 5.8475 × 1 0 − 5 kg .
Convert decigrams to kilograms: 406 dg = 0.0406 kg .
Convert centigrams to kilograms: 1900 cg = 0.019 kg .
Convert decagrams to kilograms: 945 Dg = 9.45 kg .
Convert milligrams to kilograms: 1854 mg = 0.001854 kg .
Convert tonnes to kilograms: 23 tonnes = 23000 kg .
Final answers: 5.8475 × 1 0 − 5 kg , 0.0406 kg , 0.019 kg , 9.45 kg , 0.001854 kg , 23000 kg .
5.8475 × 1 0 − 5 kg , 0.0406 kg , 0.019 kg , 9.45 kg , 0.001854 kg , 23000 kg
Explanation
Understanding the Problem and Conversion Factors We need to convert the given masses into kilograms (kg). We will use the following conversion factors:
1 microgram (μg) = 1 0 − 6 grams (g) 1 decigram (dg) = 1 0 − 1 grams (g) 1 centigram (cg) = 1 0 − 2 grams (g) 1 decagram (Dg) = 10 grams (g) 1 milligram (mg) = 1 0 − 3 grams (g) 1 tonne = 1000 kilograms (kg) 1 gram (g) = 1 0 − 3 kilograms (kg)
Performing the Conversions a) Convert 58 475 μg to kg: 58475 μ g = 58475 × 1 0 − 6 g = 58475 × 1 0 − 6 × 1 0 − 3 kg = 5.8475 × 1 0 − 5 kg
b) Convert 406 dg to kg: 406 dg = 406 × 1 0 − 1 g = 406 × 1 0 − 1 × 1 0 − 3 kg = 0.0406 kg
c) Convert 1 900 cg to kg: 1900 cg = 1900 × 1 0 − 2 g = 1900 × 1 0 − 2 × 1 0 − 3 kg = 0.019 kg
e) Convert 945 Dg to kg: 945 Dg = 945 × 10 g = 945 × 10 × 1 0 − 3 kg = 9.45 kg
f) Convert 1 854 mg to kg: 1854 mg = 1854 × 1 0 − 3 g = 1854 × 1 0 − 3 × 1 0 − 3 kg = 0.001854 kg
g) Convert 23 tonnes to kg: 23 tonnes = 23 × 1000 kg = 23000 kg
Final Results Here are the conversions: a) 58 475 μg = 5.8475 × 1 0 − 5 kg b) 406 dg = 0.0406 kg c) 1 900 cg = 0.019 kg e) 945 Dg = 9.45 kg f) 1 854 mg = 0.001854 kg g) 23 tonnes = 23000 kg
Examples
Understanding mass conversions is crucial in many real-world applications. For instance, in cooking, you might need to convert milligrams of a spice to grams for a recipe. In medicine, dosages are often prescribed in micrograms or milligrams, requiring accurate conversion to kilograms based on a patient's weight. Similarly, in construction or shipping, knowing how to convert tonnes to kilograms is essential for calculating load capacities and ensuring safety. These conversions enable precise measurements and prevent errors in various practical scenarios.
