Let’s work through the operations step by step using numbers from the list:
**Numbers from the list:**
1. 3.2 × 10^4
2. 1.95 × 10^6
3. 8.03 × 10^-8
4. 2.56 × 10^-2
5. 4.82 × 10^12
### a. Addition
**Choose 3.2 × 10^4 and 1.95 × 10^6:**
To add these numbers, we need them to have the same exponent:
1. Convert 3.2 × 10^4 to 10^6:
3.2 × 10^4 = 0.032 × 10^6
2. Now add:
0.032 × 10^6 + 1.95 × 10^6 = (0.032 + 1.95) × 10^6
= 1.982 × 10^6
### b. Subtraction
**Choose 1.95 × 10^6 and 3.2 × 10^4:**
Again, we will bring the two numbers to the same exponent:
1. Convert 3.2 × 10^4 to 10^6:
3.2 × 10^4 = 0.032 × 10^6
2. Now subtract:
1.95 × 10^6 - 0.032 × 10^6 = (1.95 - 0.032) × 10^6
= 1.918 × 10^6
### c. Multiplication
**Choose 2.56 × 10^-2 and 4.82 × 10^12:**
To multiply, multiply the coefficients and add the exponents:
1. Coefficients:
2.56 × 4.82 = 12.3072
2. Exponents:
(-2 + 12) = 10
3. Combine:
12.3072 × 10^10.
### d. Division
**Choose 4.82 × 10^12 and 1.95 × 10^6:**
To divide, divide the coefficients and subtract the exponents:
1. Coefficients:
4.82 ÷ 1.95 ≈ 2.464
2. Exponents:
(12 - 6) = 6
3. Combine:
2.464 × 10^6.
### e. Addition with a Decimal
**Choose 2.56 × 10^-2 and add it to 32.8:**
Convert 2.56 × 10^-2 to a decimal:
2.56 × 10^-2 = 0.0256
Now add:
32.8 + 0.0256 = 32.8256.
### f. Subtraction from 1,845.19
**Choose 1.95 × 10^6 and subtract from 1,845.19:**
1. Convert 1.95 × 10^6 to a decimal:
1.95 × 10^6 = 1,950,000.
2. Now subtract:
1,845.19 - 1,950,000 = -1,948,154.81.
### g. Multiplication by 256.7
**Choose 3.2 × 10^4:**
1. Coefficients:
3.2 × 256.7 ≈ 820.64.
2. Keep exponent as 10^4.
3. Combine:
820.64 × 10^4
= 8.2064 × 10^6 (shifting the decimal to maintain scientific notation).
### h. Division by 0.3
**Choose 8.03 × 10^-8:**
1. Division:
(8.03 ÷ 0.3) × 10^-8 ≈ 26.767 × 10^-8.
2. Adjust to scientific notation:
2.6767 × 10^-7.
In summary, we have performed addition, subtraction, multiplication, and division, converting where necessary for scientific notation.