‘Convert the given standard notation below to scientific notation_ Then, perform the indicated operation. Apply the rules for significant figures in your final answer. 150,000 0.0025 * 20 3,000,000 0.015 X 150’
The Correct Answer and Explanation is:
Let’s break down the problem step by step.
1. Convert the numbers to scientific notation:
We need to express each number in scientific notation.
- 150,000150,000150,000 = 1.5×1051.5 \times 10^51.5×105
- 0.00250.00250.0025 = 2.5×10−32.5 \times 10^{-3}2.5×10−3
- 202020 = 2.0×1012.0 \times 10^12.0×101 (note that 2.02.02.0 keeps one significant figure)
- 3,000,0003,000,0003,000,000 = 3.0×1063.0 \times 10^63.0×106 (again, keeping significant figures)
- 0.0150.0150.015 = 1.5×10−21.5 \times 10^{-2}1.5×10−2
- 150150150 = 1.5×1021.5 \times 10^21.5×102
2. Perform the multiplication:
Now we need to multiply all of the numbers in scientific notation. We will multiply the coefficients and add the exponents:(1.5×105)×(2.5×10−3)×(2.0×101)×(3.0×106)×(1.5×10−2)×(1.5×102)(1.5 \times 10^5) \times (2.5 \times 10^{-3}) \times (2.0 \times 10^1) \times (3.0 \times 10^6) \times (1.5 \times 10^{-2}) \times (1.5 \times 10^2)(1.5×105)×(2.5×10−3)×(2.0×101)×(3.0×106)×(1.5×10−2)×(1.5×102)
- First, multiply the coefficients: 1.5×2.5×2.0×3.0×1.5×1.5=1.5×2.5=3.751.5 \times 2.5 \times 2.0 \times 3.0 \times 1.5 \times 1.5 = 1.5 \times 2.5 = 3.751.5×2.5×2.0×3.0×1.5×1.5=1.5×2.5=3.75 3.75×2.0=7.53.75 \times 2.0 = 7.53.75×2.0=7.5 7.5×3.0=22.57.5 \times 3.0 = 22.57.5×3.0=22.5 22.5×1.5=33.7522.5 \times 1.5 = 33.7522.5×1.5=33.75 33.75×1.5=50.62533.75 \times 1.5 = 50.62533.75×1.5=50.625
So the total coefficient is 50.62550.62550.625.
- Now, add the exponents: 105×10−3×101×106×10−2×102=105−3+1+6−2+2=10910^5 \times 10^{-3} \times 10^1 \times 10^6 \times 10^{-2} \times 10^2 = 10^{5 – 3 + 1 + 6 – 2 + 2} = 10^9105×10−3×101×106×10−2×102=105−3+1+6−2+2=109
3. Combine the coefficient and exponent:
50.625×10950.625 \times 10^950.625×109
4. Adjust the coefficient:
In scientific notation, the coefficient should be between 1 and 10. We can adjust 50.62550.62550.625 as follows:50.625=5.0625×10150.625 = 5.0625 \times 10^150.625=5.0625×101
So, the final expression becomes:5.0625×101+9=5.0625×10105.0625 \times 10^{1 + 9} = 5.0625 \times 10^{10}5.0625×101+9=5.0625×1010
5. Apply significant figures:
We must apply the correct number of significant figures based on the initial values. The number with the least significant figures is 0.00250.00250.0025 which has 2 significant figures. So, we round our final result to 2 significant figures:5.0625≈5.15.0625 \approx 5.15.0625≈5.1
Thus, the final answer in scientific notation is:5.1×10105.1 \times 10^{10}5.1×1010
Conclusion:
The correct final answer, with appropriate significant figures, is:5.1×1010\boxed{5.1 \times 10^{10}}5.1×1010
