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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

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Dec 09, 2011
Convert Number to Base 4
by: Staff

Question:

in expanded form the number 323 in base 4


Answer:

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 + 3

This is usually explained to students as:

300 means 3 times 100
20 means 2 times 10
3 means 3 times 1

Each of these numbers in the expanded format is a POWER OF 10:

300 = 3 × 100 = 3×10²
20 = 2 × 10 = 2×10¹
3 = 3 × 1 = 3×10⁰ (remember that 10⁰ = 1)

The expanded form can be written as:

323 = 300 + 20 + 3
323 = 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 + 3×10⁰

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

Now 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) + 3

The remainder of 3 belongs in the 4⁰ column, which will be: 3×4⁰


80 = (4 × 20) + 0

The remainder of 0 belongs in the 4¹ column, which will be: 0×4¹ + 3×4⁰


20 = (4 × 5) + 0

The remainder of 0 belongs in the 4² column, which will be: 0×4² + 0×4¹ + 3×4⁰


5 = (4 × 1) + 1

The remainder of 1 belongs in the 4³ column, which will be: 1×4³ + 0×4² + 0×4¹ + 3×4⁰


4 = (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 + 3×4⁰


323 = 1×4⁴ + 1×4³ + 0×4² + 0×4¹ + 3×4⁰ = 11003

323(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 + 3×4⁰

323 = 256 + 64 + 0 + 0 + 3

323 = 323, OK → 323(number base 4) = 11003 is VALID




You 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.html






Thanks for writing.

Staff
www.solving-math-problems.com



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