Answer :
Sure, let's break down each of the questions and solve them step-by-step.
### c) Questions
1. How much water is left in the tank if 1.8 x 10 litres of water is used up?
- The question isn't quite clear about the initial amount of water in the tank, but we'll assume the tank initially contains 1.8 x 10 litres.
- Initial water = [tex]\( 1.8 \times 10 = 18 \)[/tex] litres
- Water used = [tex]\( 1.8 \times 10 = 18 \)[/tex] litres
- Water left in the tank = Initial water - Water used = 18 - 18 = 0 litres
2. Sound travels [tex]\( 3.43 \times 10^2 \)[/tex] metres in 1 second. Calculate the distance travelled by sound in [tex]\( 3.6 \times 10^3 \)[/tex] seconds.
- Speed of sound = [tex]\( 3.43 \times 10^2 = 343 \)[/tex] metres/second
- Time = [tex]\( 3.6 \times 10^3 = 3600 \)[/tex] seconds
- Distance travelled = Speed × Time = [tex]\( 343 \times 3600 = 1234800 \)[/tex] metres
- Distance travelled in scientific notation = [tex]\( 1.2348 \times 10^6 \)[/tex] metres
3. How many petrol tanks of capacity [tex]\( 1.2 \times 10 \)[/tex] litres each are required to empty [tex]\( 4.8 \times 10^5 \)[/tex] litres of petrol?
- Capacity per tank = [tex]\( 1.2 \times 10 = 12 \)[/tex] litres
- Total petrol = [tex]\( 4.8 \times 10^5 = 480000 \)[/tex] litres
- Number of tanks required = Total petrol / Capacity per tank = [tex]\( \frac{480000}{12} = 40000 \)[/tex] tanks
- Number of tanks in scientific notation = [tex]\( 4 \times 10^4 \)[/tex] tanks
4. The speed of light in vacuum is [tex]\( 2.99 \times 10^5 \)[/tex] km/s. Calculate the distance travelled by light in [tex]\( 3.6 \times 10^3 \)[/tex] seconds.
- Speed of light = [tex]\( 2.99 \times 10^5 = 299000 \)[/tex] km/second
- Time = [tex]\( 3.6 \times 10^3 = 3600 \)[/tex] seconds
- Distance travelled = Speed × Time = [tex]\( 299000 \times 3600 = 1076400000 \)[/tex] km
- Distance travelled in scientific notation = [tex]\( 1.0764 \times 10^9 \)[/tex] km
### Additional Sections
1. Distance from Earth to the 7 planets:
- To find the exact distances, you would typically visit NASA's official website or other astronomical databases to get the most current data.
2. Body weight in grams and milligrams, then in scientific notation:
- Example: If your body weight is 70 kg:
- In grams: [tex]\( 70 \times 10^3 = 70000 \)[/tex] grams
- In milligrams: [tex]\( 70 \times 10^6 = 70000000 \)[/tex] milligrams
- Scientific notation for grams: [tex]\( 7 \times 10^4 \)[/tex] grams
- Scientific notation for milligrams: [tex]\( 7 \times 10^7 \)[/tex] milligrams
3. Write any two 7-digit and 9-digit numerals and express them in scientific notation:
- 7-digit numerals:
1. 1234567 = [tex]\( 1.234567 \times 10^6 \)[/tex]
2. 7654321 = [tex]\( 7.654321 \times 10^6 \)[/tex]
- 9-digit numerals:
1. 123456789 = [tex]\( 1.23456789 \times 10^8 \)[/tex]
2. 987654321 = [tex]\( 9.87654321 \times 10^8 \)[/tex]
4. Write any two decimal numbers with 6 and 7 decimal places, then express them in scientific notation:
- Decimal numbers:
1. 0.00000123 = [tex]\( 1.23 \times 10^{-6} \)[/tex]
2. 0.000000987 = [tex]\( 9.87 \times 10^{-7} \)[/tex]
5. How is the scientific notation of numbers useful in numeration or measurements?
- Benefits of Scientific Notation:
- Simplifies large/small number representation: Easily express very large numbers (like the distance between stars) or very small numbers (like the size of atoms).
- Makes calculations manageable: Simplifies multiplication and division by allowing the combination of exponents.
- Reduces error: Reduces the chances of error when dealing with multiple zeros in standard form.
- Universally understood: Provides a common ground for scientific communication across various fields and languages.
Feel free to ask for any further clarifications or additional questions!
### c) Questions
1. How much water is left in the tank if 1.8 x 10 litres of water is used up?
- The question isn't quite clear about the initial amount of water in the tank, but we'll assume the tank initially contains 1.8 x 10 litres.
- Initial water = [tex]\( 1.8 \times 10 = 18 \)[/tex] litres
- Water used = [tex]\( 1.8 \times 10 = 18 \)[/tex] litres
- Water left in the tank = Initial water - Water used = 18 - 18 = 0 litres
2. Sound travels [tex]\( 3.43 \times 10^2 \)[/tex] metres in 1 second. Calculate the distance travelled by sound in [tex]\( 3.6 \times 10^3 \)[/tex] seconds.
- Speed of sound = [tex]\( 3.43 \times 10^2 = 343 \)[/tex] metres/second
- Time = [tex]\( 3.6 \times 10^3 = 3600 \)[/tex] seconds
- Distance travelled = Speed × Time = [tex]\( 343 \times 3600 = 1234800 \)[/tex] metres
- Distance travelled in scientific notation = [tex]\( 1.2348 \times 10^6 \)[/tex] metres
3. How many petrol tanks of capacity [tex]\( 1.2 \times 10 \)[/tex] litres each are required to empty [tex]\( 4.8 \times 10^5 \)[/tex] litres of petrol?
- Capacity per tank = [tex]\( 1.2 \times 10 = 12 \)[/tex] litres
- Total petrol = [tex]\( 4.8 \times 10^5 = 480000 \)[/tex] litres
- Number of tanks required = Total petrol / Capacity per tank = [tex]\( \frac{480000}{12} = 40000 \)[/tex] tanks
- Number of tanks in scientific notation = [tex]\( 4 \times 10^4 \)[/tex] tanks
4. The speed of light in vacuum is [tex]\( 2.99 \times 10^5 \)[/tex] km/s. Calculate the distance travelled by light in [tex]\( 3.6 \times 10^3 \)[/tex] seconds.
- Speed of light = [tex]\( 2.99 \times 10^5 = 299000 \)[/tex] km/second
- Time = [tex]\( 3.6 \times 10^3 = 3600 \)[/tex] seconds
- Distance travelled = Speed × Time = [tex]\( 299000 \times 3600 = 1076400000 \)[/tex] km
- Distance travelled in scientific notation = [tex]\( 1.0764 \times 10^9 \)[/tex] km
### Additional Sections
1. Distance from Earth to the 7 planets:
- To find the exact distances, you would typically visit NASA's official website or other astronomical databases to get the most current data.
2. Body weight in grams and milligrams, then in scientific notation:
- Example: If your body weight is 70 kg:
- In grams: [tex]\( 70 \times 10^3 = 70000 \)[/tex] grams
- In milligrams: [tex]\( 70 \times 10^6 = 70000000 \)[/tex] milligrams
- Scientific notation for grams: [tex]\( 7 \times 10^4 \)[/tex] grams
- Scientific notation for milligrams: [tex]\( 7 \times 10^7 \)[/tex] milligrams
3. Write any two 7-digit and 9-digit numerals and express them in scientific notation:
- 7-digit numerals:
1. 1234567 = [tex]\( 1.234567 \times 10^6 \)[/tex]
2. 7654321 = [tex]\( 7.654321 \times 10^6 \)[/tex]
- 9-digit numerals:
1. 123456789 = [tex]\( 1.23456789 \times 10^8 \)[/tex]
2. 987654321 = [tex]\( 9.87654321 \times 10^8 \)[/tex]
4. Write any two decimal numbers with 6 and 7 decimal places, then express them in scientific notation:
- Decimal numbers:
1. 0.00000123 = [tex]\( 1.23 \times 10^{-6} \)[/tex]
2. 0.000000987 = [tex]\( 9.87 \times 10^{-7} \)[/tex]
5. How is the scientific notation of numbers useful in numeration or measurements?
- Benefits of Scientific Notation:
- Simplifies large/small number representation: Easily express very large numbers (like the distance between stars) or very small numbers (like the size of atoms).
- Makes calculations manageable: Simplifies multiplication and division by allowing the combination of exponents.
- Reduces error: Reduces the chances of error when dealing with multiple zeros in standard form.
- Universally understood: Provides a common ground for scientific communication across various fields and languages.
Feel free to ask for any further clarifications or additional questions!
