Question

State the number of significant figures in each of the following. (a) 70 (This is a measurement rather than a count.) (b) 9.7 104 (c) 9.70 104 (d) 7.09 104 (e) 7.090 104 (f) 0.0097 (g) 0.079 (h) 0.0907

Answer 1

The significant figures of a number are those digits that carry meaning contributing to its measurement resolution. This includes all digits except:  

All leading zeros;

Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures);

Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.

(a) 70 : Significant digit =7
Only one significant digit.

(b) 9.7104 : All non-zero numbers are always significant. All zeroes which are simultaneously to the right of the decimal point and at the end of the number are significant.
Hence, the number of significant digits is 5.

(c) 9.70104 : The number of significant digits is 6.

(d) 7.09104 : All the digits are significant. (no leading and trailing zero)
No. of significant digits = 6

(e) 7.090104 : All the digits are significant. (no leading and trailing zero)
No. of significant digits = 7

(f) 0.0097 : Significant digits = 97
No. of significant digits = 2

(g) 0.079 : Significant digits = 79 , No. of significant digits = 2

(h) 0.0907 : Significant digits =6032
No. of sig. digits = 3