How to Convert Fractions to Exponential Notation

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Mathematical equations commonly include either fractions or exponential notations, although they are both quite different concepts. Fractions describe a numerical value using a ratio of two numbers, such as 3/4. Exponential notation (sometimes also called scientific notation) has a different purpose: It multiplies a numerical value by 10 raised to a power to make the number easier to write. Instead of writing 10,000,000 for example, you could use exponential notation and write 1 x 10^7. You can convert an expression from a fraction to exponential notation by first calculating the decimal value of the fraction.

    Change the fraction into a decimal number by dividing the top portion of the fraction (the numerator) by the bottom portion (the denominator). For example, in the case of the fraction 2/50, you would divide 2 by 50 to get a result of 0.04.

    Rewrite the number you just calculated, shifting the position of the decimal point of the number either left or right enough spaces so that the number is changed into a value equal to or greater than 1 but less than 10. In the example, you would move the decimal point two spaces to the right and rewrite 0.04 as 4 because 4 is greater than 1 but less than 10.

    Multiply the new value you just wrote by 10 raised to the power of "x" where x is the number of spaces that you had to move the decimal point. If you had to move the decimal point to the right, make x negative; otherwise, make it positive. Following these rules, the example value of 4 would be multiplied by 10 raised to the power of -2 to yield 4 x 10^-2. This is the equivalent of the fraction 2/50, expressed in exponential notation.


    • Some fractions will not give a finite decimal number when divided. In these cases, you will have to write an approximate decimal number. For example, the fraction 1/3 could be written as 0.333, even though it actually has an infinite series of 3's after the decimal point.


About the Author

Michael Judge has been writing for over a decade and has been published in "The Globe and Mail" (Canada's national newspaper) and the U.K. magazine "New Scientist." He holds a Master of Science from the University of Waterloo. Michael has worked for an aerospace firm where he was in charge of rocket propellant formulation and is now a college instructor.

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