Express 0.314 in scientific notation.
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Enter the coefficient in the green box and the exponent in the yellow box.
Coefficient (green)
$\square$
Answer (2)
To express 0.314 in scientific notation, we move the decimal point one place to the right to get 3.14, making the exponent -1 because we moved it right. Thus, 0.314 can be expressed as 3.14 × 1 0 − 1 .
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Move the decimal point in 0.314 one place to the right to obtain 3.14.
Since the original number is less than 1, the exponent of 10 will be negative.
The exponent is -1 because we moved the decimal point one place to the right.
Therefore, 0.314 in scientific notation is 3.14 × 1 0 − 1 .
Explanation
Understanding Scientific Notation We are asked to express the number 0.314 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 0.314 to scientific notation, we need to move the decimal point one place to the right to get the number 3.14, which is between 1 and 10.
Determining the Exponent Since we moved the decimal point one place to the right, we need to multiply 3.14 by 1 0 − 1 to get the original number 0.314. Therefore, 0.314 = 3.14 × 1 0 − 1 .
Final Answer Thus, 0.314 expressed in scientific notation is 3.14 × 1 0 − 1 .
Examples
Scientific notation is used in many areas, such as physics, astronomy, and chemistry, to express very large or very small numbers. For example, the speed of light is approximately 3.0 × 1 0 8 meters per second, and the mass of an electron is approximately 9.11 × 1 0 − 31 kilograms. Using scientific notation makes it easier to work with these numbers and compare their magnitudes. Imagine calculating the distance to a star in meters, which might be 5.6 × 1 0 20 meters. Scientific notation simplifies these calculations and makes the numbers more manageable.
