### A good answer might be:

| Decimal | Binary so far
Start | 0.750 | 0.
×2 | 1.50 | 0.1
erase | .50 | 0.1
×2 | 1.00 | 0.11
erase | .00 | 0.11
Result |  | 0.11

So `0.7510 = 0.112`.

To check this, go in the other direction: `0.112 = 2-1 + 2-2 = 0.5 + 0.25 = 0.75`

# Non-terminating Result

| Decimal | Binary so far
Start | 0.1 | 0.
×2 | 0.2 | 0.0
×2 | 0.4 | 0.00
×2 | 0.8 | 0.000
×2 | 1.6 | 0.0001
| .6 | 0.0001
×2 | 1.2 | 0.00011
| 0.2 | 0.00011
×2 | 0.4 | 0.000110
×2 | 0.8 | 0.0001100
×2 | 1.6 | 0.00011001
| .6 | 0.00011001
×2 | 1.2 | 0.000110011
| 0.2 | 0.000110011
×2 | 0.4 | 0.0001100110
×2 | 0.8 | 0.00011001100
Result |  | 0.00011001100...

At right the algorithm used to convert `0.110` to binary.

The algorithm does not end. After it has started up, the same pattern `0.2, 0.4, 0.8, 1.6, 0.6, 1.2, 0.2` repeats endlessly. The pattern `0011` is appended to the growing binary fraction for each repitition.

> Unexpected Fact: The value "one tenth" cannot be represented precisely using a binary fraction.

This is true in the base two positional notation used here, and also in floating point representation used in programming languages. This is sometimes an important consideration when high accuracy is needed.

### QUESTION 15:

Can "one third" be represented accurately in decimal?