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Example 1.3: Rounding Numbers

Round the following to the indicated number of significant figures:
(a) 31.57 (to two significant figures)
(b) 8.1649 (to three significant figures)
(c) 0.051065 (to four significant figures)
(d) 0.90275 (to four significant figures)
In PQcalc, the easiest way to round is to multiply by 1. If you want two significant figures, multiply by 1.0 (which has two significant figures), if you want three significant figures, multiply by 1.00 (which has three significant figures), and so on.

Solution

\(a\) \(= 31.57\)


\(a_{\mathrm{2sigfig}}\) \(= a \cdot 1.0\)

\(\ \ \ =31.57 \cdot 1.0\)

\(\ \ \ =32.\)


\(b\) \(= 8.1649\)


\(b_{\mathrm{3sigfig}}\) \(= b \cdot 1.00\)

\(\ \ \ =8.1649 \cdot 1.00\)

\(\ \ \ =8.16\)


\(c\) \(= 0.051065\)


\(c_{\mathrm{4sigfig}}\) \(= c \cdot 1.000\)

\(\ \ \ =0.051065 \cdot 1.000\)

\(\ \ \ =0.05106\)


\(d\) \(= 0.90275\)


\(d_{\mathrm{4sigfig}}\) \(= d \cdot 1.000\)

\(\ \ \ =0.90275 \cdot 1.000\)

\(\ \ \ =0.9028\)


(a) 31.57 rounds “up” to 32 (the dropped digit is 5, and the retained digit is even)
(b) 8.1649 rounds “down” to 8.16 (the dropped digit, 4, is less than 5)
(c) 0.051065 rounds “down” to 0.05106 (the dropped digit is 5, and the retained digit is even)
(d) 0.90275 rounds “up” to 0.9028 (the dropped digit is 5, and the retained digit is even)