What is $5,900,000$ in scientific notation?
A. $5.9 \times 10^{-5}$
B. $5.9 \times 10^7$
C. $5.9 \times 10^{-6}$
D. $5.9 \times 10^6$
Answer (2)
Express 5 , 900 , 000 in the form a × 1 0 b , where 1 ≤ a < 10 .
Move the decimal point 6 places to the left to get 5.9 .
Multiply 5.9 by 1 0 6 since we moved the decimal point 6 places to the left.
The scientific notation for 5 , 900 , 000 is 5.9 × 1 0 6 .
Explanation
Understanding Scientific Notation We are asked to express the number 5 , 900 , 000 in scientific notation. Scientific notation is a way of writing numbers as a product of a number between 1 and 10 and a power of 10.
Moving the Decimal Point To convert 5 , 900 , 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 6 places to the left to get 5.9 .
Determining the Exponent Since we moved the decimal point 6 places to the left, we multiply 5.9 by 1 0 6 to get 5.9 × 1 0 6 .
Final Result Therefore, 5 , 900 , 000 in scientific notation is 5.9 × 1 0 6 .
Selecting the Correct Option Comparing our result with the given options, we see that option D, 5.9 × 1 0 6 , is the correct answer.
Examples
Scientific notation is extremely useful in fields like astronomy and physics, where dealing with very large or very small numbers is common. For example, the distance to the nearest star, Proxima Centauri, is approximately 40,208,000,000,000 kilometers. Writing this in scientific notation as 4.0208 × 1 0 13 km makes it much easier to handle and understand. Similarly, the mass of an electron is approximately 0.00000000000000000000000000000091093837 kg, which can be written in scientific notation as 9.1093837 × 1 0 − 31 kg.
The number 5 , 900 , 000 can be expressed in scientific notation as 5.9 × 1 0 6 by moving the decimal point 6 places to the left. The correct answer to the multiple-choice question is option D. 5.9 × 1 0 6 .
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