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Scientific NotationConverting From Expanded Form to Scientific NotationHereâ€™s how to convert a number from expanded form to scientific notation.
Procedure â€” To Convert From Expanded Form to Scientific Notation Step 1 Move the decimal point until there is only one nonzero digit to its left. Step 2 Write the number from Step 1 multiplied by a power of 10. To find the power, count the number of places you moved the decimal point.
Step 3 Check the sign of the power.
Example 1 The distance from the sun to the earth is approximately 93,000,000 miles. Write 93,000,000 in scientific notation. Solution
Step 3 Check the sign of the power. The original number is greater than 10, so the power should be positive, and it is. We can also check our result by expanding 9.3 Ã— 10^{7}.
Thus, 93,000,000 miles = 9.3 Ã— 10^{7} miles.
Example 2 The rest mass of an electron is approximately 0.000000000000000000000000000000911 kg. Write this number in scientific notation. Solution Step 1 Move the decimal point until there is only one nonzero digit to its left. Move the decimal point until it is between the 9 and the 1. Step 2 Write the number from Step 1 multiplied by a power of 10. We moved the decimal point 31 places to the right. So the power of 10 is -31.Step 3 Check the sign of the power. The original number is less than1, so the power should be negative, and it is. Thus, 0.000000000000000000000000000000911 kg = 9.11 Ã— 10^{-31} kg. |