Question E.3: Determining the Number of Significant Figures in a Number H...
Determining the Number of Significant Figures in a Number
How many significant figures are in each number?
(a) 0.04450 m (b) 5.0003 km (c) 10 dm = 1 m (d) 1.000 × 10^5 s (e) 0.00002 mm (f) 10,000 m
(a) 0.04450 m Four significant figures. The two 4s and the 5 are significant (Rule 1). The trailing zero is after a decimal point and is therefore significant (Rule 4). The leading zeroes only mark the decimal place and are therefore not significant (Rule 3).
(b) 5.0003 km Five significant figures. The 5 and 3 are significant (Rule 1), as are the three interior zeroes (Rule 2).
(c) 10 dm = 1 m Unlimited significant figures. Defined quantities have an unlimited number of significant figures.
(d) 1.000 × 10^5 s Four significant figures. The 1 is significant (Rule 1). The trailing zeroes are after a decimal point and therefore significant (Rule 4).
(e) 0.00002 mm One significant figure. The 2 is significant (Rule 1). The leading zeroes only mark the decimal place and are therefore not significant (Rule 3).
(f) 10,000 m Ambiguous. The 1 is significant (Rule 1), but the trailing zeroes occur before an implied decimal point and are therefore ambiguous (Rule 4). Without more information, you would assume one significant figure. It is better to write this as 1 \times 10^5 to indicate one significant figure or as 1.000 × 10^5 to indicate five (Rule 4).