Which expression is equivalent to the given expression?
(9 × 10^6) / (1 × 10^−8) + (3 × 10^−8)
A. 2.25 × 10^14
B. 3 × 10^14
C. 2.25 × 10^−2
D. 3 × 10^2
Which expression is equivalent to the given expression?
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Let’s simplify the given expression step by step:
1. Start with the first part of the expression:
[(9 × 10^6) / (1 × 10^{-8})]
When dividing, you can subtract the exponents:
[
= 9 × 10^{6 – (-8)} = 9 × 10^{6 + 8} = 9 × 10^{14}
]
2. Now, we’ll add the second part of the expression:
[9 × 10^{14} + (3 × 10^{-8})]
Since (10^{-8}) is much smaller than (10^{14}), you can ignore it for the sake of addition. However, if you want to express everything in the same power of ten, we would convert (3 × 10^{-8}) to the same base:
[
= 9 × 10^{14} + 0.00000003 × 10^{14} = 9 × 10^{14} + 0.00000003 × 10^{14} = (9 + 0.00000003) × 10^{14} approx 9 × 10^{14}
]
Therefore, this addition does not significantly change the result.
3. As a result, the simplified expression approximately equals (9 × 10^{14}).
Given the