Determine the difference of $3.2 \times 10^{10}-1.1 \times 10^{10}$. Write your answer in scientific notation.
A) $4.3 \times 10^{10}$
B) $2.1 \times 10^0$
C) $2.1 \times 10^{10}$
D) $4.3 \times 10^0$
Answer (2)
Subtract the coefficients: 3.2 − 1.1 = 2.1 .
Keep the exponent the same: 1 0 10 .
Write the result in scientific notation: 2.1 × 1 0 10 .
The final answer is 2.1 × 1 0 10 .
Explanation
Understanding the Problem We are asked to find the difference between two numbers expressed in scientific notation: 3.2 × 1 0 10 and 1.1 × 1 0 10 . The result must be expressed in scientific notation.
Setting up the Subtraction To find the difference, we subtract the two numbers: 3.2 × 1 0 10 − 1.1 × 1 0 10 . Since both numbers have the same power of 10, we can factor out 1 0 10 and subtract the coefficients: ( 3.2 − 1.1 ) × 1 0 10 .
Calculating the Difference Now, we calculate the difference of the coefficients: 3.2 − 1.1 = 2.1 .
Expressing the Result in Scientific Notation Therefore, the result in scientific notation is 2.1 × 1 0 10 .
Final Answer Comparing the result with the given options, we see that option C matches our result.
Examples
Scientific notation is extremely useful in various fields, such as physics, astronomy, and engineering, to represent very large or very small numbers. For instance, the distance to a star or the size of an atom can be conveniently expressed using scientific notation. Imagine you are calculating the total memory of a large data center. If each server has 6.4 × 1 0 12 bytes of memory and there are 10 servers, the total memory is 6.4 × 1 0 13 bytes. This makes calculations and comparisons much easier than dealing with long strings of digits.
The difference of the two numbers in scientific notation is 2.1 × 10^{10}. This matches option C from the choices provided. Therefore, the correct answer is C.
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