How to Convert Fractions to Exponential Notation


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.

Things You'll Need

  • Calculator
  • 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.

Tips & Warnings

  • 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.


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