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In this lesson, students learn that a number is in scientific notation if it composed of a whole number or decimal between 1 and 10, times a power of ten. For example, 4.13 x 10^8 is in scientific notation. To convert a number from scientific notation to standard notation, note that a positive exponent means that the decimal point is moved to the right, and a negative exponent means that the decimal point is moved to the left. For example, to convert 4.13 x 10^8 to standard notation, since the exponent is positive 8, move the decimal 8 places to the right, to get 413,000,000.

To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point, so here we have 6.42000. (Notice that there now is only one digit to the left of the decimal point.) Next, count the number of places that we would need to move the decimal point in order to get back to the original number, 642,000. Since we would need to move the decimal point 5 places to the right to get back to the original number, 642,000, we would need to multiply 6.42000 times 10 to the 5th power. Notice that our exponent is positive. That's because we needed to move the exponent to the right to get back to the original number. So 642,000 can be written in scientific notation as 6.42000 times 10 to the 5th power, or 6.42 times 10 to the 5th power. Remember that we can drop any zeros at the end of the decimal.

Tagged under: Scientific,Notation,Convert,standard,notation,solve,conversion,math,practice,problems

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