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Calculate 4.8 X 10^-3 -9.4X10^-6. Express the answer in scientific notation rounding to 2 decimal places

11 answers

To calculate \( 4.8 \times 10^{-3} - 9.4 \times 10^{-6} \), we need to express both numbers with the same exponent.

  1. Convert \( 4.8 \times 10^{-3} \) into \( 10^{-6} \) scale: \[ 4.8 \times 10^{-3} = 4.8 \times 10^{-3} \times \frac{1000}{1000} = 4.8 \times 1000 \times 10^{-6} = 4800 \times 10^{-6} \]

  2. Now we can subtract: \[ 4800 \times 10^{-6} - 9.4 \times 10^{-6} = (4800 - 9.4) \times 10^{-6} = 4790.6 \times 10^{-6} \]

  3. Convert \( 4790.6 \times 10^{-6} \) to scientific notation: \[ 4790.6 = 4.7906 \times 10^{3} \] Therefore: \[ 4790.6 \times 10^{-6} = 4.7906 \times 10^{3} \times 10^{-6} = 4.7906 \times 10^{-3} \]

  4. Round to two decimal places: \[ 4.7906 \approx 4.79 \text{ (after rounding)} \]

Thus, the final answer in scientific notation is: \[ \boxed{4.79 \times 10^{-3}} \]

A strand of hair has an average mass of 2.17 X 10^-5 ounces. A grain of rice has an average mass of
0.002 ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in
scientific notation.(1 point)

__ X __ ounces

To find out how much heavier a grain of rice is than a strand of hair, you can perform the subtraction:

  1. Convert the mass of rice to scientific notation: The mass of a grain of rice is given as \(0.002\) ounces, which can be expressed in scientific notation as: \[ 0.002 = 2.0 \times 10^{-3} \text{ ounces} \]

  2. Use the mass of the strand of hair: The mass of a strand of hair is already given as: \[ 2.17 \times 10^{-5} \text{ ounces} \]

  3. Perform the subtraction: We will convert both numbers to the same exponent to make the subtraction easier. Let's convert \(2.0 \times 10^{-3}\) to the same exponent as \(2.17 \times 10^{-5}\):

    To convert \(2.0 \times 10^{-3}\) to \(10^{-5}\): \[ 2.0 \times 10^{-3} = 2.0 \times 10^{-3} \times \frac{100}{100} = 200.0 \times 10^{-5} \]

  4. Now subtract: \[ 200.0 \times 10^{-5} - 2.17 \times 10^{-5} = (200.0 - 2.17) \times 10^{-5} = 197.83 \times 10^{-5} \]

  5. Convert \(197.83 \times 10^{-5}\) to scientific notation: \[ 197.83 = 1.9783 \times 10^{2} \] So, \[ 197.83 \times 10^{-5} = 1.9783 \times 10^{2} \times 10^{-5} = 1.9783 \times 10^{-3} \]

  6. Express it in scientific notation and round it (if necessary): While \(1.9783\) is not rounded, we can round it to two decimal places if needed: \[ 1.9783 \approx 1.98 \]

Thus, the final answer, representing how much heavier a grain of rice is than a strand of hair in scientific notation, is: \[ \boxed{1.98 \times 10^{-3}} \text{ ounces} \]

Light travels at an approximate rate of 1.9 X 10^5 mi./sec. There are about 3.2 X 10^7 seconds in a
year. About how many miles does light travel in a year? Write the answer in scientific notation.
Express the answer to the exact decimal place.(1 point)

To find out how far light travels in a year, we will multiply the speed of light by the number of seconds in a year.

  1. Given values:

    • Speed of light: \(1.9 \times 10^5\) miles/second
    • Number of seconds in a year: \(3.2 \times 10^7\) seconds/year

  2. Multiply the two values: \[ \text{Distance} = (1.9 \times 10^5) \times (3.2 \times 10^7) \]

  3. Multiply the coefficients: \[ 1.9 \times 3.2 = 6.08 \]

  4. Add the exponents: \[ 10^5 \times 10^7 = 10^{5 + 7} = 10^{12} \]

  5. Combine the results: \[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]

The answer in scientific notation, expressed to the exact decimal place, is: \[ \boxed{6.08 \times 10^{12}} \text{ miles} \]

Light travels at an approximate rate of mi./sec. There are about seconds in a
year. About how many miles does light travel in a year? Write the answer in scientific notation.
Express the answer to the exact decimal place.(1 point)

__ Miles

It seems that some numbers are missing from your question. Specifically, the speed of light in miles per second and the number of seconds in a year are not provided. However, typically:

  • The speed of light is approximately \(1.9 \times 10^5\) miles per second.
  • The number of seconds in a year is approximately \(3.2 \times 10^7\) seconds.

Based on this typical information, we can calculate the distance that light travels in one year as follows:

  1. Given values:

    • Speed of light: \(1.9 \times 10^5\) miles/second
    • Number of seconds in a year: \(3.2 \times 10^7\) seconds/year

  2. Multiply the two values: \[ \text{Distance} = (1.9 \times 10^5) \times (3.2 \times 10^7) \]

  3. Multiply the coefficients: \[ 1.9 \times 3.2 = 6.08 \]

  4. Add the exponents: \[ 10^5 \times 10^7 = 10^{5 + 7} = 10^{12} \]

  5. Combine the results: \[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]

So, light travels approximately: \[ \boxed{6.08 \times 10^{12}} \text{ miles in a year.} \]

If you provide the specific numbers, I can recalculate accordingly.

is that correct?

Yes, based on the typical values provided, the calculation is correct. Here’s a step-by-step verification of the calculation:

  1. Speed of Light: \(1.9 \times 10^5\) miles/second.
  2. Number of Seconds in a Year: Approximately \(3.2 \times 10^7\) seconds/year.

Calculation:

\[ \text{Distance} = (\text{Speed of Light}) \times (\text{Seconds in a Year}) \]

Substituting in the values:

\[ \text{Distance} = (1.9 \times 10^5) \times (3.2 \times 10^7) \]

Step 1: Multiply the coefficients:

\[ 1.9 \times 3.2 = 6.08 \]

Step 2: Add the exponents:

\[ 10^5 \times 10^7 = 10^{5 + 7} = 10^{12} \]

Final Calculation:

Combine the results:

\[ \text{Distance} = 6.08 \times 10^{12} \text{ miles} \]

Conclusion:

Therefore, light travels approximately \(6.08 \times 10^{12}\) miles in one year when using the above values for the speed of light and the seconds in a year.

If you have any specific values or if any details were different, please provide them, and I can recalculate accordingly. Otherwise, the value of \(6.08 \times 10^{12}\) miles is indeed correct with the given data.

The average tectonic plate moves at the rate of 0.006 m per year. How many meters would it move in 2 X 10^6 years? Write the answer in scientific notation expressed to the exact decimal place

To find out how far a tectonic plate moves in \(2 \times 10^6\) years, you can utilize the formula:

\[ \text{Distance} = \text{Rate} \times \text{Time} \]

  1. Given values:

    • Rate: \(0.006 , \text{m/year}\)
    • Time: \(2 \times 10^6 , \text{years}\)

  2. Substituting the values into the formula:

\[ \text{Distance} = (0.006 , \text{m/year}) \times (2 \times 10^6 , \text{years}) \]

  1. Calculating the coefficients:

\[ 0.006 \times 2 = 0.012 \]

  1. Since there are no exponents in the rate, the exponent from the time remains:

Thus, we can write:

\[ \text{Distance} = 0.012 , \text{m} \]

  1. Convert \(0.012\) into scientific notation:

To convert \(0.012\) into scientific notation, we write it as:

\[ 0.012 = 1.2 \times 10^{-2} \]

  1. Combine it with the unit:

Thus, the distance the tectonic plate moves in \(2 \times 10^6\) years is:

\[ \text{Distance} = 1.2 \times 10^{-2} , \text{meters} \]

So, the final answer in scientific notation, expressed to the exact decimal place, is:

\[ \boxed{1.2 \times 10^{-2}} \text{ meters} \]