To evaluate the expression \( 10^{12} + 3 \times 10^{8} + 9 \times 10^{5} + 10 \), let's break it down step by step.
Convert the terms into scientific notation:
- \( 10^{12} \) is already in scientific notation.
- \( 3 \times 10^{8} \) is also in scientific notation.
- \( 9 \times 10^{5} \) is in scientific notation.
- \( 10 \) can be expressed as \( 1 \times 10^{1} \).
Put all terms over a common power of 10, if necessary:
- We could express everything in terms of \( 10^{12} \):
- \( 10^{12} \) remains \( 10^{12} \).
- Converting \( 3 \times 10^{8} \) to the same power: \[ 3 \times 10^{8} = 0.00003 \times 10^{12} \]
- Converting \( 9 \times 10^{5} \): \[ 9 \times 10^{5} = 0.0000009 \times 10^{12} \]
- Converting \( 10 \) to the same power: \[ 10 = 0.00000000001 \times 10^{12} \]
- We could express everything in terms of \( 10^{12} \):
Add the terms together: \[ 10^{12} + 0.00003 \times 10^{12} + 0.0000009 \times 10^{12} + 0.00000000001 \times 10^{12} \] Finding the sum: \[ = (1 + 0.00003 + 0.0000009 + 0.00000000001) \times 10^{12} \] = \( 1.000030900001 \times 10^{12} \)
Round and express in scientific notation: If we look at \( 1.000030900001 \times 10^{12} \), this simplifies approximately to: \[ 1.000031 \times 10^{12} \]
Now, the statement \( 1.000301 \times 10^{12} \) given in your original equation seems potentially inaccurate based on the computation we just performed. \( 1.000301 \times 10^{12} \) suggests that the sum of additional terms would significantly change the result, which appears not to be happening here.
Conclusively, the original addition outcome is approximately \( 1.000031 \times 10^{12} \) based on our breakdown of each term.