# Truncation Error vs Rounding Error¶

Copyright (C) 2010-2020 Luke Olson

Copyright (C) 2020 Andreas Kloeckner

## MIT License

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In this notebook, we'll investigate two common sources of error: Truncation error and rounding error.

```
import numpy as np
import matplotlib.pyplot as pt
```

**Task:** Approximate a function (here: a parabola, by a line)

```
center = -1
width = 6
def f(x):
return - x**2 + 3*x
def df(x):
return -2*x + 3
grid = np.linspace(center-width/2, center+width/2, 100)
fx = f(grid)
pt.plot(grid, fx)
pt.plot(grid, f(center) + df(center) * (grid-center))
pt.xlim([grid[0], grid[-1]])
pt.ylim([np.min(fx), np.max(fx)])
```

(-28.0, 2.2497704315886136)

- What's the error we see?
- What if we make
`width`

smaller?

```
```