How to Compare Scientific Notations
Scientific notation is used to denote very large or very small numbers by showing the power of 10 that a number between 1 and 9 is raised to equal the large or small number. Large numbers like 3,400,000,000,000 use positive powers and are written as 3.4 x 10^12. Small numbers like 0.0000000000000045 use negative powers and are written as 4.5 x 10^-15. Scientific notation also conserves space.
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Instructions
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Identity the power that each number is being raised to. For example, if you are comparing 7.0 x 10^55 with 3.5 x 10^50, the power of the first number is 55 and the power of the second number is 50.
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Subtract the second power from the first power. In the example: 55 - 50 = 5.
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Determine which number is greater. If the result is positive, the first number is greater. If the result is negative, the first number is smaller. Since the result in the example is positive 5, the first number, 7.0 x 10^55, is greater than the second number, 3.5 x 10^50.
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Determine approximately how many times greater or smaller the first number is. Insert it for x in the function 10^x. For example, since the result is 5, plug in 5 for x and you get 10^5, or 100,000. This means the first number is about 100,000 times larger than the second number.
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Determine which number is greater if the two numbers are raised to the same power of 10. The number with the larger decimal is the greater number. For example, if you are comparing 6.4 x 10^28 and 7.9 x 10^28, since both are raised to the same power, 7.9 x 10^28 is greater because 7.9 is greater than 6.4
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