Answer :
Sure! Let's break down each of the given expressions step-by-step to convert them from scientific notation to standard form.
### Part (a) [tex]\(2.7 \times 10^3\)[/tex]
1. Identify the base number: 2.7
2. Identify the power of 10, which is 10^3.
3. The power 3 indicates we need to move the decimal point 3 places to the right.
- Starting with 2.7 -> Moving the decimal one place to get 27.0 -> Moving the decimal two places to get 270.0 -> Moving the decimal three places gives us 2700.0
4. Therefore, [tex]\(2.7 \times 10^3\)[/tex] is equal to 2700.0.
### Part (b) [tex]\(4.5 \times 10^4\)[/tex]
1. Identify the base number: 4.5
2. Identify the power of 10, which is 10^4.
3. The power 4 indicates we need to move the decimal point 4 places to the right.
- Starting with 4.5 -> Moving the decimal one place to get 45.0 -> Moving the decimal two places to get 450.0 -> Moving the decimal three places to get 4500.0 -> Moving the decimal four places gives us 45000.0
4. Therefore, [tex]\(4.5 \times 10^4\)[/tex] is equal to 45000.0.
### Part (c) [tex]\(7.56 \times 10^5\)[/tex]
1. Identify the base number: 7.56
2. Identify the power of 10, which is 10^5.
3. The power 5 indicates we need to move the decimal point 5 places to the right.
- Starting with 7.56 -> Moving the decimal one place to get 75.6 -> Moving the decimal two places to get 756.0 -> Moving the decimal three places to get 7560.0 -> Moving the decimal four places to get 75600.0 -> Moving the decimal five places gives us 756000.0
4. Therefore, [tex]\(7.56 \times 10^5\)[/tex] is equal to 756000.0.
In summary, the conversions are:
- [tex]\(2.7 \times 10^3 = 2700.0\)[/tex]
- [tex]\(4.5 \times 10^4 = 45000.0\)[/tex]
- [tex]\(7.56 \times 10^5 = 756000.0\)[/tex]
These are the numbers expressed in standard form.
### Part (a) [tex]\(2.7 \times 10^3\)[/tex]
1. Identify the base number: 2.7
2. Identify the power of 10, which is 10^3.
3. The power 3 indicates we need to move the decimal point 3 places to the right.
- Starting with 2.7 -> Moving the decimal one place to get 27.0 -> Moving the decimal two places to get 270.0 -> Moving the decimal three places gives us 2700.0
4. Therefore, [tex]\(2.7 \times 10^3\)[/tex] is equal to 2700.0.
### Part (b) [tex]\(4.5 \times 10^4\)[/tex]
1. Identify the base number: 4.5
2. Identify the power of 10, which is 10^4.
3. The power 4 indicates we need to move the decimal point 4 places to the right.
- Starting with 4.5 -> Moving the decimal one place to get 45.0 -> Moving the decimal two places to get 450.0 -> Moving the decimal three places to get 4500.0 -> Moving the decimal four places gives us 45000.0
4. Therefore, [tex]\(4.5 \times 10^4\)[/tex] is equal to 45000.0.
### Part (c) [tex]\(7.56 \times 10^5\)[/tex]
1. Identify the base number: 7.56
2. Identify the power of 10, which is 10^5.
3. The power 5 indicates we need to move the decimal point 5 places to the right.
- Starting with 7.56 -> Moving the decimal one place to get 75.6 -> Moving the decimal two places to get 756.0 -> Moving the decimal three places to get 7560.0 -> Moving the decimal four places to get 75600.0 -> Moving the decimal five places gives us 756000.0
4. Therefore, [tex]\(7.56 \times 10^5\)[/tex] is equal to 756000.0.
In summary, the conversions are:
- [tex]\(2.7 \times 10^3 = 2700.0\)[/tex]
- [tex]\(4.5 \times 10^4 = 45000.0\)[/tex]
- [tex]\(7.56 \times 10^5 = 756000.0\)[/tex]
These are the numbers expressed in standard form.
