Scientists estimate that Earth is 4,540,000,000 years old. What is that number expressed in scientific notation?
A. $4.54 \times 10^7$
B. $4.54 \times 10^9$
C. $454 \times 10^{10}$
D. $2(127 \times 10^7)$
Answer (2)
Convert the number to the form a × 1 0 b , where 1 ≤ a < 10 .
Move the decimal point in 4 , 540 , 000 , 000 nine places to the left to get 4.54 .
Since the decimal point was moved 9 places to the left, the exponent is 9, so the number in scientific notation is 4.54 × 1 0 9 .
The final answer is 4.54 × 1 0 9 .
Explanation
Understanding Scientific Notation We are given the number 4 , 540 , 000 , 000 and asked to express it in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 (including 1 but excluding 10) and a power of 10.
Moving the Decimal Point To convert 4 , 540 , 000 , 000 to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we move the decimal point 9 places to the left to get 4.54 .
Determining the Exponent Since we moved the decimal point 9 places to the left, we multiply 4.54 by 1 0 9 to get the original number. Therefore, the scientific notation for 4 , 540 , 000 , 000 is 4.54 × 1 0 9 .
Identifying the Correct Option Comparing our result to the given options, we see that option B, 4.54 × 1 0 9 , matches our answer.
Final Answer Therefore, the number 4 , 540 , 000 , 000 expressed in scientific notation is 4.54 × 1 0 9 .
Examples
Scientific notation is used in many fields, such as astronomy, physics, and chemistry, to express very large or very small numbers. For example, the distance to the nearest star, Proxima Centauri, is approximately 40 , 200 , 000 , 000 , 000 kilometers. In scientific notation, this is 4.02 × 1 0 13 kilometers. Similarly, the mass of an electron is approximately 0.000000000000000000000000000000911 kilograms. In scientific notation, this is 9.11 × 1 0 − 31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes.
The number 4,540,000,000 expressed in scientific notation is 4.54 × 1 0 9 . The correct answer choice from the options provided is B. This conversion involves moving the decimal point nine places to the left to create a number between 1 and 10, which gives us the exponent of 9.
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