The last section was to get you used to counting in a different system of numbers.

 Let's take a look at how base eight comapres to base ten.

Remember when we looked at the number 1,234 in base ten? We noticed that you could rewrite 1,234 as:

1*1000 + 2*100+ 3*10 + 4*1

1
2
3
4
1000s place
100s place
10s place
1s place

In base eight, however,1,234 has an entirely different meaning.

In base eight, you have

1
2
3
4
512s place
64s place
8s place
1s place

This turns over after eight groups of eight groups of eight! This place tells us how many groups of 512 there are.

This turns over after eight groups of eight! This place tells us how many groups of 64 there are.

Since we turn over after "7", this place tells us how many groups of 8 we have!

This stays the same.

Or: 83=512

Or: 82=64

Or: 81=8

Or: 80=1

Important!

The only difference between base ten numbers and any numbers of any other base is that the "places" are just powers of different numbers.

So, if we want to translate "1, 234" (base 8) into base 10, we could rewrite 1,234 as:

1*512 + 2*64 + 3*8 +1*1

=512 + 128 + 24 +1

=665

Here's another example:

Translate 943 (base eight) into its base ten equivalent.

Step1: multiply down

9
4
3
64s place
8s place
1s place
9*64=576
4*8=32
3*1=3

Step two: add across
576+32+3=611 in base ten.

Question 4:

Using the above as an example, translate these base eight numbers into base 10 numbers!

a) 62 in base eight equals _________ in base ten.

b) 146 in base eight equals _________ in base ten.

c) 2405 in base eight equals _________ in base ten.

d) 24134 in base eight equals _________ in base ten.