Express 727,000 in scientific notation.
[?] \times 10^[?]
Enter the coefficient in the green box and the exponent in the yellow box.
Answer (2)
Move the decimal point in 727,000 to obtain a number between 1 and 10, which is 7.27.
Count the number of places the decimal point was moved, which is 5.
Express 727,000 in scientific notation as the product of 7.27 and 1 0 5 .
The final answer is 7.27 × 1 0 5 .
Explanation
Understanding Scientific Notation We need to express 727,000 in scientific notation, which is a way of writing numbers as a product of a number between 1 and 10 (including 1) and a power of 10.
Moving the Decimal Point To convert 727,000 to scientific notation, we first identify the decimal point, which is at the end of the number. We then move the decimal point to the left until we have a number between 1 and 10. In this case, we move the decimal point 5 places to the left to get 7.27.
Determining the Exponent Since we moved the decimal point 5 places to the left, the exponent of 10 will be 5. Therefore, 727,000 in scientific notation is 7.27 × 1 0 5 .
Final Answer So, the coefficient is 7.27 and the exponent is 5.
Examples
Scientific notation is used in many real-world applications, especially in science and engineering, to represent very large or very small numbers. For example, the distance from the Earth to the Sun is approximately 149,600,000,000 meters, which can be written in scientific notation as 1.496 × 1 0 11 meters. Similarly, the size of a virus might be 0.00000002 meters, which can be written as 2 × 1 0 − 8 meters. Using scientific notation makes it easier to work with these numbers and compare their magnitudes.
727,000 can be expressed in scientific notation as 7.27 × 10^5, where 7.27 is the coefficient and 5 is the exponent. The decimal point is moved five places to the left to achieve this format. This method makes it easier to work with large numbers.
;
