INFORMATION

DECIMAL TO BASE 5 CONVERSION

WHOLE NUMBERS

We apply the following rules to convert a decimal number to base 5.

• We divide the decimal number by 5 repeatedly until the quotient becomes 0.
• Starting at the least significant digit, we write the remainders in the same order of divisions.

For example, to convert decimal 42 to base 5, we divide 42 by 5 repeatedly until the quotient becomes 0.

When we divide 42 by 5, the quotient is 8 and the remainder is 2. Thus, 2 is the least significant digit of the base 5 equivalent. We continue the algorithm with 8. When we divide 8 by 5, the quotient is 1 and the remainder is 3. Then 3 is the second least significant digit of the base 5 number. Finally, we divide 1 by 5. When we do this operation, the quotient is 0 and the remainder is 1. Because the quotient is 0, we stop the procedure. Then we write the last remainder to the most significant digit of the base 5 number. To sum up, the base 5 representation of 42 is 132.

(42)₁₀ = (132)₅

DECIMAL NUMBERS

In case, the decimal number is not an integer, we can convert the whole number and fractional parts separately and add the base 5 equivalents up.

To convert the fractional part of a decimal number, we apply the following rules.

• We multiply the fractional part by 5 repeatedly until the product becomes an integer or the number of significant digits is sufficient for our calculations.
• At each step, we write the integer part of the rightmost digit to the fractional part of the base 5 number. We continue with the fractional part of the product.

For example, to convert 42.304 to base 5, we multiply the fractional part by 5 repeatedly until we find an integer.

• 0.304 × 5 = 1.52
• 0.52 × 5 = 2.6
• 0.6 × 5 = 3

The fractional part of 42.304 is 0.304. When we multiply 0.304 by 5, the result is 1.52. The integer part of 1.52 is 1. Thus we write 1 to the first digit on the RHS of the radix point.

0.1

We continue with the fractional part of 1.52. When we multiply 0.52 by 5, the result is 2.6. We write the integer part of 2.6 to the next digit of the base 5 number.

0.12

The fractional part of 2.6 is 0.6. Therefore, we continue with this number. The product of 0.6 and 5 is equal to 3. Because 3 is an integer we write it to the next digit of the base 5 number and stop multiplications.

(0.304)₁₀ = (0.123)₅

Base 5 representation of 42.304 is equal to the sum of base 5 representations of 42 and 0.304. Thus, decimal 42.304 is equal to 132.123 in base 5.

(42.304)₁₀ = (42)₁₀ + (0.304)₁₀

= (132)₅ + (0.123)₅

= (132.123)₅

WHAT IS DECIMAL TO BASE 5 CONVERTER?

Decimal to base 5 converter,

• Computes the base 5 equivalent of the entered decimal number and
• Describes each step of the conversion for both whole number and fractional parts,

HOW TO USE DECIMAL TO BASE 5 CONVERTER?

You can use decimal to base 5 converter in two ways.

• USER INPUTS

  

  You can enter a decimal number to the input box and click on the "CONVERT" button. The result and explanations appaer below the calculator

• RANDOM INPUTS

  

  You can click on the DIE ICON next to the input box. If you use this property, a random decimal number is generated and entered to the calculator, automatically. You can see the result and explanations below the calculator. You can create your own examples and practice using this property.

• CLEARING THE INPUT BOX

  

  To check the base 5 equivalent of other decimals you can clear the input box by clicking on the CLEAR button under the input box.

• COPYING & DOWNLOADING THE SOLUTION

  • 

    You can copy the generated solution by clicking on the "Copy Text" link, appaers under the solution panel.

  • 

    Even you can download the solution as an image file with .jpg extension if you click on the "Download Solution" link at the bottom of the solution panel. You can share the downloaded image file.