Express 727,000 in scientific notation.
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Enter the coefficient in the green box and the exponent in the yellow box.
Coefficient (green)
Answer (2)
727,000 can be expressed in scientific notation as 7.27 × 10^5. This is done by moving the decimal point 5 places to the left to form the coefficient 7.27 and determining the exponent based on the number of moves. Therefore, the answer is 7.27 in the coefficient box and 5 in the exponent box.
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Convert the number to have one non-zero digit to the left of the decimal point: 7.27 .
Count the number of places the decimal point was moved: 5.
Express the number in scientific notation: $7.27
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 (the coefficient) and a power of 10.
Finding the Coefficient To convert 727,000 to scientific notation, we 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 is 5.
Final Scientific Notation Therefore, 727,000 in scientific notation is 7.27 × 1 0 5 .
Examples
Scientific notation is useful in many real-world situations, especially when dealing with very large or very small numbers. For example, astronomers use scientific notation to express the distances between stars and galaxies. A distance of 150,000,000,000 meters can be written as 1.5 × 1 0 11 meters. Similarly, scientists use it to express the size of atoms or the mass of molecules. This notation simplifies calculations and makes it easier to compare numbers of vastly different sizes.
