How To Convert Other Bases To Base 10

To convert other bases to base 10, follow the same method explained on how to convert base 2 to base 10.

In this lesson, you will learn the step-by-step method for converting other bases to base 10.

BONUS: A link to practice questions on number bases is included at the end of this lesson.

Question on converting other bases to base 10

Let’s take an example:

Question:

Convert 2445 to a number in base 10

STEP 1.

Write out each digit in the given base

2

4

4

STEP 2.

Put a multiplication sign and the base in front of each digit

2 × 5

4 × 5

4 × 5

TAKE NOTE: (do NOT multiply yet)

STEP 3.

Starting with the last digit as ZERO, raise each base to the power of its position

2 × 52

4 × 51

4 × 50

STEP 4.

Calculate the “power” first (according to BODMAS)

2 × 25

4 × 5

4 × 1 (Law of Indices)

STEP 5.

Then multiply next

2 × 25 = 50

4 × 5 = 20

4 × 1 = 4

STEP 6.

Add your answers together

50 + 20 + 4

= 74

FINAL ANSWER:

244 (in base five)

= 74 (in base ten)

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Otherwise,

Click the button to practice questions on number bases.

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