# Math - Convert Number to Base 4

in expanded form the number 323 in base4

The only difference between a number base of 10 and a base of 4 is: EVERY DIGIT WILL BE A POWER OF 4.

323(number base 10) = 3×10² + 2×10¹ + 3×10⁰

323(number base 4) = ?×4⁴ + ?×4³ + ?×4² + ?×4¹ + ?×4⁰

### Comments for Math - Convert Number to Base 4

 Dec 09, 2011 Convert Number to Base 4 by: Staff Question:in expanded form the number 323 in base 4Answer:To understand the number base 5, it’s probably easiest to begin by reviewing the way the number base 10 works.Write the number 323 in expanded form using the number base 10.The answer is: 300 + 20 + 3This is usually explained to students as:300 means 3 times 10020 means 2 times 103 means 3 times 1Each of these numbers in the expanded format is a POWER OF 10:300 = 3 × 100 = 3×10²20 = 2 × 10 = 2×10¹3 = 3 × 1 = 3×10⁰ (remember that 10⁰ = 1)The expanded form can be written as:323 = 300 + 20 + 3323 = 3×10² + 2×10¹ + 3×10⁰ If we switch our number base to 4 instead of 10, we can apply the same idea. The only difference will be, EVERY DIGIT WILL BE A POWER OF 4.323(number base 10) = 3×10² + 2×10¹ + 3×10⁰323(number base 4) = ?×4⁴ + ?×4³ + ?×4² + ?×4¹ + ?×4⁰Now that you know what the number 323 will look like in base 4, you can find the numbers to replace the question marks.To find missing numbers, use the REMAINDER METHOD.Using the Remainder Method to convert 323 to base 4:323 = (4 × 80) + 3The remainder of 3 belongs in the 4⁰ column, which will be: 3×4⁰80 = (4 × 20) + 0The remainder of 0 belongs in the 4¹ column, which will be: 0×4¹ + 3×4⁰20 = (4 × 5) + 0The remainder of 0 belongs in the 4² column, which will be: 0×4² + 0×4¹ + 3×4⁰5 = (4 × 1) + 1The remainder of 1 belongs in the 4³ column, which will be: 1×4³ + 0×4² + 0×4¹ + 3×4⁰4 = (4 × 1)There is ONE remaining 4. The ONE belongs in the 4⁴ column, which will be: 1×4⁴ + 1×4³ + 0×4² + 0×4¹ + 3×4⁰323 = 1×4⁴ + 1×4³ + 0×4² + 0×4¹ + 3×4⁰ = 11003323(number base 4) = 11003 The final answer is: 323(number base 4) = 11003 Check the answer for accuracy:323(number base 4) = 11003 323 = 1×4⁴ + 1×4³ + 0×4² + 0×4¹ + 3×4⁰323 = 256 + 64 + 0 + 0 + 3323 = 323, OK → 323(number base 4) = 11003 is VALIDYou can also check your answers (converting from base 10 to base 4) by going to the following web site:http://www.unitconversion.org/numbers/base-10-to-base-4-conversion.htmlThanks for writing.Staff www.solving-math-problems.com

 Nov 10, 2017 Response NEW by: John To Thank you so much!