Convert the following: 1. 2 kg to t 2. 5 000 g to kg 3. 650 g to mg 4. 50 t to g 5. 8 g to kg 6. 0,001 kg to g 7. 4,2 tons to kg 8. 3,1 mg to g 9. 6,21 g to t 10. 82,7 mg to kg Calculations between units of mass
The Correct Answer and Explanation is:
Let’s break down each conversion step by step:
1. 2 kg to t
1 tonne (t) = 1,000 kilograms (kg), so:2 kg=21000=0.002 t2 \, \text{kg} = \frac{2}{1000} = 0.002 \, \text{t}2kg=10002=0.002t
Answer: 0.002 t
2. 5,000 g to kg
1 kilogram (kg) = 1,000 grams (g), so:5,000 g=5,0001000=5 kg5,000 \, \text{g} = \frac{5,000}{1000} = 5 \, \text{kg}5,000g=10005,000=5kg
Answer: 5 kg
3. 650 g to mg
1 gram (g) = 1,000 milligrams (mg), so:650 g=650×1,000=650,000 mg650 \, \text{g} = 650 \times 1,000 = 650,000 \, \text{mg}650g=650×1,000=650,000mg
Answer: 650,000 mg
4. 50 t to g
1 tonne (t) = 1,000,000 grams (g), so:50 t=50×1,000,000=50,000,000 g50 \, \text{t} = 50 \times 1,000,000 = 50,000,000 \, \text{g}50t=50×1,000,000=50,000,000g
Answer: 50,000,000 g
5. 8 g to kg
1 kilogram (kg) = 1,000 grams (g), so:8 g=81000=0.008 kg8 \, \text{g} = \frac{8}{1000} = 0.008 \, \text{kg}8g=10008=0.008kg
Answer: 0.008 kg
6. 0.001 kg to g
1 kilogram (kg) = 1,000 grams (g), so:0.001 kg=0.001×1,000=1 g0.001 \, \text{kg} = 0.001 \times 1,000 = 1 \, \text{g}0.001kg=0.001×1,000=1g
Answer: 1 g
7. 4.2 tons to kg
1 ton (t) = 1,000 kilograms (kg), so:4.2 t=4.2×1,000=4,200 kg4.2 \, \text{t} = 4.2 \times 1,000 = 4,200 \, \text{kg}4.2t=4.2×1,000=4,200kg
Answer: 4,200 kg
8. 3.1 mg to g
1 milligram (mg) = 0.001 grams (g), so:3.1 mg=3.1×0.001=0.0031 g3.1 \, \text{mg} = 3.1 \times 0.001 = 0.0031 \, \text{g}3.1mg=3.1×0.001=0.0031g
Answer: 0.0031 g
9. 6.21 g to t
1 gram (g) = 0.000001 tonnes (t), so:6.21 g=6.21×10−6=0.00000621 t6.21 \, \text{g} = 6.21 \times 10^{-6} = 0.00000621 \, \text{t}6.21g=6.21×10−6=0.00000621t
Answer: 0.00000621 t
10. 82.7 mg to kg
1 milligram (mg) = 1 × 10⁻⁶ kilograms (kg), so:82.7 mg=82.7×10−6=0.0000827 kg82.7 \, \text{mg} = 82.7 \times 10^{-6} = 0.0000827 \, \text{kg}82.7mg=82.7×10−6=0.0000827kg
Answer: 0.0000827 kg
Explanation:
Unit conversions rely on known equivalences between units. When converting between mass units, it’s crucial to use the proper factor (e.g., 1 kg = 1,000 g) and apply it to get the result. Here are some key relationships that you’ll use for mass conversions:
- 1 kilogram (kg) = 1,000 grams (g)
- 1 tonne (t) = 1,000 kilograms (kg)
- 1 milligram (mg) = 0.001 grams (g)
- 1 tonne (t) = 1,000,000 grams (g)
By applying these relationships, the conversions become straightforward multiplications or divisions. For instance, to convert 650 grams to milligrams, we multiply by 1,000. Similarly, converting grams to kilograms involves dividing by 1,000. These unit conversion principles apply in a consistent manner, making them easy to apply for a variety of mass units.
