$(2.3 \times 10^{-5})(3.1 \times 10^{12}) =$
A) $7.13 \times 10^7$
B) $5.4 \times 10^7$
C) $7.13 \times 10^{-60}$
D) $5.4 \times 10^8$
Answer (1)
Multiply the coefficients: 2.3 im es 3.1 = 7.13 .
Multiply the powers of 10: 1 0 − 5 t im es 1 0 12 = 1 0 7 .
Combine the results: 7.13 t im es 1 0 7 .
The final answer is 7.13 t im es 1 0 7 .
Explanation
Understanding the Problem We are given the expression ( 2.3 × 1 0 − 5 ) ( 3.1 × 1 0 12 ) . We need to simplify this expression and choose the correct answer from the options provided.
Simplifying the Expression To simplify the expression, we multiply the coefficients and add the exponents of 10.
Multiplying Coefficients First, multiply the coefficients: 2.3 × 3.1 = 7.13 .
Multiplying Powers of 10 Next, multiply the powers of 10: 1 0 − 5 × 1 0 12 = 1 0 − 5 + 12 = 1 0 7 .
Combining Results Now, combine the results: ( 2.3 × 3.1 ) × 1 0 7 = 7.13 × 1 0 7 .
Choosing the Correct Option Comparing the result 7.13 × 1 0 7 with the given options, we see that it matches option A.
Final Answer Therefore, the answer is 7.13 × 1 0 7 .
Examples
Scientific notation is used in many fields, such as physics, astronomy, and engineering, to represent very large or very small numbers. For example, the distance to a star can be expressed in scientific notation, making it easier to work with than writing out all the zeros. Similarly, the size of an atom can be expressed in scientific notation.
