Accurate to n Significant Figures/Examples/Pi to 5 Figures

Example of Accurate to $n$ Significant Figures

The constant pi ($\pi$) expressed accurate to $5$ significant figures is:

$\pi \approx 3 \cdotp 1416$

Proof

We start with the decimal expansion of $\pi$:

The decimal expansion of $\pi$ starts:

$\pi \approx 3 \cdotp 14159 \, 26535 \, 89793 \, 23846 \, 26433 \, 83279 \, 50288 \, 41971 \ldots$

We note that:

$3.1416 - 3.14159 < 3.14159 \ldots - 3.1415$

and so $\pi$ rounded to $5$ significant figures is:

$3.1416$

$\blacksquare$

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): accurate or correct: 1. (accurate to $n$ significant digits)