Math 8A Unit 4 Study Guide
12. The average plate tectonic plate moves at the rate of 0.006 meter 3 * 10 ^ 6 per year. How many meters would it move in years? Write the answer in scientific notation, expressed to the exact decimal place
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To find the total distance the plate tectonic plate moves in years, we need to multiply the rate by the number of years.
Rate: 0.006 meter 3 * 10 ^ 6 per year
Let's assume we want to find the distance it moves in 5 years.
Distance = Rate * time
Distance = (0.006 meter 3 * 10 ^ 6 per year) * (5 years)
To multiply these numbers, we can multiply the coefficients (0.006 * 5) and add the exponents (3 + 6):
Distance = 0.030 meter * 10 ^ (3 + 6) per year
Simplifying the exponent:
Distance = 0.030 meter * 10 ^ 9 per year
The answer, in scientific notation, is 0.030 * 10^9 meters per year.
To find the distance the tectonic plate would move in years, we can multiply the rate of movement (0.006 meter per year) by the number of years.
0.006 m/yr * 3 * 10^6 yr = 0.006 * 3 * 10^6 m
Multiplying 0.006 by 3 gives us 0.018, and simplifying 10^6 gives us 1,000,000.
So, the tectonic plate would move 0.018 * 1,000,000 meters.
This can be expressed in scientific notation as 1.8 * 10^5 meters.
To find the number of meters the tectonic plate would move in a given number of years, we can use the formula:
Distance = Rate * Time
In this case, the rate is 0.006 meter/year and we want to find the distance in years. Let's substitute these values into the formula:
Distance = 0.006 meter/year * (3 * 10^6 years)
Now, let's simplify the expression:
Distance = 0.006 * 3 * 10^6 meter
To multiply these numbers, we can multiply the decimals first and then multiply the exponent separately:
Distance = 0.018 * 10^6 meter
To express this in scientific notation, we express 0.018 as 1.8 x 10^(-2) and leave the exponent unchanged:
Distance = 1.8 x 10^(-2) * 10^6 meter
Now, to multiply the numbers with the same base, we can add the exponents:
Distance = 1.8 x 10^(6-2) meter
Simplifying further:
Distance = 1.8 x 10^4 meter
Therefore, the tectonic plate would move 1.8 x 10^4 meters in a given number of years.