1 | initial version |

You can have a look at https://floating-point-gui.de/

The reason is that floating-point numbers are multiple of a (negative) power of 2, and since `0.2=1/5`

, it can not be represented exactly.

Actually, none of `14 * 1.2`

nor `16.8`

are exact, but the cancellation in the sum luckilly leads to zero, so the correct result results from two errors, see:

```
sage: a = 16.8
sage: a.exact_rational()
4728779608739021/281474976710656
sage: a.sign_mantissa_exponent()
(1, 4728779608739021, -48)
```

2 | No.2 Revision |

You can have a look at https://floating-point-gui.de/

The reason is that floating-point numbers are multiple of a (negative) power of 2, and since $0.2=1/5$, it can not be represented `0.2=1/5`

, ~~exactly.~~exactly (the equality $1/5 = k/2^m$ has no integer solution in $k$ and $m$).

Actually, none of `14 * 1.2`

nor `16.8`

are exact, but the cancellation in the sum luckilly leads to zero, so the correct result results from two errors, see:

```
sage: a = 16.8
sage: a.exact_rational()
4728779608739021/281474976710656
sage: a.sign_mantissa_exponent()
(1, 4728779608739021, -48)
```

3 | No.3 Revision |

You can have a look at https://floating-point-gui.de/

The reason is that floating-point numbers are multiple of a (negative) power of 2, and since $0.2=1/5$, it can not be represented exactly (the equality $1/5 = ~~k/2^m$ ~~m/2^e$ has no integer solution in ~~$k$ ~~$m$ and ~~$m$).~~$a$).

Actually, none of `14 * 1.2`

nor `16.8`

are exact, but the cancellation in the sum luckilly leads to zero, so the correct result results from two errors, see:

```
sage: a = 16.8
sage: a.exact_rational()
4728779608739021/281474976710656
sage: a.sign_mantissa_exponent()
(1, 4728779608739021, -48)
```

4 | No.4 Revision |

You can have a look at https://floating-point-gui.de/

The reason is that floating-point numbers are multiple of a (negative) power of 2, and since $0.2=1/5$, it can not be represented exactly (the equality $1/5 = m/2^e$ has no integer solution in $m$ and ~~$a$).~~$e$).

`14 * 1.2`

nor `16.8`

are exact, but the cancellation in the sum luckilly leads to zero, so the correct result results from two errors, see:

```
sage: a = 16.8
sage: a.exact_rational()
4728779608739021/281474976710656
sage: a.sign_mantissa_exponent()
(1, 4728779608739021, -48)
```

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