2.56x10-^2 x 1.95x10^6. show your work
4.82x10^12÷8.03x10-^8. show your work
1.95-1,84.19. show your work
3.2x10^4 x 256.7. show your work
2.56x10-^2 ÷ 0.3. show your work
To solve these equations, we will use the rules of scientific notation.
1) 2.56x10^-2 x 1.95x10^6:
Multiply the decimal parts: 2.56 x 1.95 = 4.992
Add the exponents: -2 + 6 = 4
So the answer is 4.992x10^4.
2) 4.82x10^12 ÷ 8.03x10^-8:
Divide the decimal parts: 4.82 ÷ 8.03 = 0.599503725
Subtract the exponents: 12 - (-8) = 20
So the answer is 0.599503725x10^20.
3) 1.95-1,84.19:
This expression seems to be incorrect. If you meant to subtract 1.95 from 84.19, the result is 84.19 - 1.95 = 82.24.
4) 3.2x10^4 x 256.7:
Multiply the decimal parts: 3.2 x 256.7 = 819.04
Add the exponents: 4 + 0 = 4
So the answer is 819.04x10^4.
5) 2.56x10^-2 ÷ 0.3:
Divide the decimal parts: 2.56 ÷ 0.3 = 8.53333...
Subtract the exponents: -2 - 0 = -2
So the answer is 8.53333...x10^-2.
1) To multiply numbers in scientific notation, you multiply the coefficients and add the exponents.
In this case, we have:
(2.56 × 10^(-2)) × (1.95 × 10^(6))
Multiplying the coefficients gives us:
2.56 × 1.95 = 4.992
Adding the exponents gives us:
10^(-2) × 10^(6) = 10^(-2+6) = 10^4
Therefore, the result is:
4.992 × 10^4
2) To divide numbers in scientific notation, you divide the coefficients and subtract the exponents.
In this case, we have:
(4.82 × 10^(12)) ÷ (8.03 × 10^(-8))
Dividing the coefficients gives us:
4.82 ÷ 8.03 = 0.599
Subtracting the exponents gives us:
10^(12) ÷ 10^(-8) = 10^(12-(-8)) = 10^(12+8) = 10^20
Therefore, the result is:
0.599 × 10^20
3) To subtract decimal numbers, align them by their decimal points and subtract each column starting from the right.
In this case, we have:
1.95
- 1.84
________
0.11
Therefore, the result is 0.11.
4) To multiply a decimal number with a number in scientific notation, multiply the decimal number with the coefficient, and add the exponents.
In this case, we have:
(3.2 × 10^(4)) × 256.7
Multiplying the coefficient gives us:
3.2 × 256.7 = 821.44
Adding the exponents gives us:
10^(4) × 1 = 10^(4+0) = 10^4
Therefore, the result is:
821.44 × 10^4
5) To divide a number in scientific notation by a decimal number, divide the coefficient by the decimal number, and subtract the exponents.
In this case, we have:
(2.56 × 10^(-2)) ÷ 0.3
Dividing the coefficient gives us:
2.56 ÷ 0.3 = 8.53
Subtracting the exponents gives us:
10^(-2) ÷ 1 = 10^(-2-0) = 10^(-2)
Therefore, the result is:
8.53 × 10^(-2)
Sure! Here are the step-by-step solutions to your questions:
1. To multiply (2.56x10^-2) by (1.95x10^6):
- Multiply the coefficients: 2.56 x 1.95 = 4.992
- Add the exponents: -2 + 6 = 4
- The final answer is 4.992x10^4
2. To divide (4.82x10^12) by (8.03x10^-8):
- Divide the coefficients: 4.82 ÷ 8.03 = 0. six decimal places
- Subtract the exponents: 12 - (-8) = 20
- The final answer is 0.6x10^20
3. To subtract 1.95 from 184.19:
- Align the decimal points: 184.19 - 1.95 = 182.24
4. To multiply (3.2x10^4) by 256.7:
- Multiply the coefficients: 3.2 x 256.7 = 819.84
- Add the exponents: 4 + 2 = 6
- The final answer is 819.84x10^6 or 8.1984x10^8
5. To divide (2.56x10^-2) by 0.3:
- Divide the coefficients: 2.56 ÷ 0.3 = 8.53...
- Subtract the exponents: -2 - 0 = -2
- The final answer is 8.53...x10^-2