How to Convert Decimal Fractions to Hexadecimal


A "decimal fraction" is defined as a fraction which has a base-10 denominator such as 10, 100, 1000 and so forth. Rather than base-10, "hexadecimals" are based on base-16 mathematics. In the base-10 system, a combination of only 10 characters, zero through nine, are used. With the hexadecimal base-16 system, a combination of 16 characters, zero through nine plus alphabets A through F, are used to represent numerical values. As is generally the case with calculators, converting a decimal fraction to its hexadecimal equivalent is more complicated to work out by hand than it is to figure out with a calculator.

By Hand

  • Write down the decimal fraction. For example, 5,902 / 10.

  • Divide the fraction's numerator (top or first number) by its denominator (bottom or last number). The result is the decimal equivalent of the fraction. For example, 5,902 / 10 = 590.2. Drop anything after the decimal point (if applicable). For example, 590.2 becomes 590.

  • Divide the result by 16. For example, 590 / 16 = 36 with a remainder of 14. The quotient, if greater than 0, must be divided again. Every remainder represents a hexadecimal number according to the following chart. With a remainder of 14, "E" is the hexadecimal number in this example.

  • Keep dividing the quotient by 16 until the result is less than 0. For example, 36 / 16 = 2 with a remainder of 4, and 2 / 16 = 0.125. When the quotient is less than 0, proceed to the next step.

  • Multiply the quotient by 16. For example, 0.125 * 16 = 2. The product represents a hexadecimal number.

  • Write the hexadecimal number. In the example outlined, the hexadecimal equivalent of 5,902 / 10 is 24E.

Using the Microsoft Scientific Calculator

  • Open the "Start" menu, then click "All Programs," "Accessories," then "Calculator" to launch the Microsoft Calculator.

  • Click the "View" tab and select "Scientific."

  • Enter the fraction's numerator then press the divide key. For example, enter 5902 and press "/" for division.

  • Enter the fraction's denominator then press the equal key. For example, enter 10 then press "=" for the result. The result is the decimal equivalent of the fraction.

  • Click on the "Hex" radio button to convert to decimal to hexadecimal format.

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