Evaluate the expression: \( \frac{1.5 \times 10^{11} \text{ m}}{3 \times 10^{8} \text{ m/s}} = 500 \text{ s} \)
Answer (2)
The given expression 3 × 1 0 8 m/s 1.5 × 1 0 11 m evaluates to 500 s after performing the division of the coefficients and the powers of ten. The meters cancel out, leaving us with seconds as the final unit. Therefore, the calculation is accurate.
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To solve the expression 3 × 1 0 8 m/s 1.5 × 1 0 11 m = 500 s , let's break down the steps.
This expression is asking how long, in seconds, it takes to cover a distance of 1.5 × 1 0 11 m at a constant speed of 3 × 1 0 8 m/s .
Identify the Formula: The general formula for calculating time when distance and speed are known is: Time = Speed Distance
Substitute the Given Values: Plug the known values into the formula: Time = 3 × 1 0 8 m/s 1.5 × 1 0 11 m
Divide the Coefficients: Divide the coefficients (1.5 by 3): 3 1.5 = 0.5
Subtract the Exponents of 10 (if necessary): Since you are dividing, you subtract the exponent of the denominator from the exponent of the numerator: 1 0 11 − 1 0 8 = 1 0 3
Combine Results: Combine the results of the division and the exponent subtraction: 0.5 × 1 0 3 s = 500 s
Conclusion: Therefore, the time it takes is 500 s .
This calculation demonstrates how exponential notation can simplify processes involving large numbers, often used in scientific fields such as physics. In this context, this could be an example of finding the time it takes for light to travel a particular distance, such as from the sun to Earth.
