How To Convert Other Bases To Base 10

Would you like to know how to convert from other bases to base ten in Mathematics?

In this lesson,

You will see and learn the step-by-step method for converting other bases to base 10.


ALSO SEE: How To Convert From Base Ten To Other Bases


Take note.

A link for you to practice past questions on number base 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

1. Write out each digit in the given base

2

4

4

2. Put a multiplication sign in front of each digit

2 ×

4 ×

4 ×

3. Put the given base in front of the multiplication signs

2 × 5

4 × 5

4 × 5

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

2 × 52

4 × 51

4 × 50

5. Calculate the “power” first (according to BODMAS)

2 × 25

4 × 5

4 × 1 (Law of Indices)

6. Multiply next

2 × 25 = 50

4 × 5 = 20

4 × 1 = 4

7. Add your answers together

50 + 20 + 4

= 74

FINAL ANSWER:

244 (in base five)

= 74 (in base ten)

Test yourself

Click on the link below to practice past questions on Number Base now.

  • PRACTICE QUESTIONS

GOOD LUCK.

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