Question

State the number of significant figures in the following : 
(a) 0.007 m² (b) 2.64 × 1024 kg (c) 0.2370 g cm^–3 (d) 6.320 J (e) 6.032 N m^–2 (f) 0.0006032 m²

Answer 1

Quick Rules for Significant Figures

• All non-zero digits are significant
• Zeros between non-zero digits are significant
• Trailing zeros after decimal point are significant
• Leading zeros before non-zero digits are not significant
• Trailing zeros in whole numbers without decimal are ambiguous

Analysis of Given Measurements

Measurement	Breakdown	Significant Figures	Count
\(0.007 \, \text{m}^2\)	Leading zeros (0.00) not significant Only 7 is significant	7	1
\(2.64 \times 10^{24} \, \text{kg}\)	Scientific notation: 2.64 has 3 digits Exponent \(10^{24}\) exact	2.64	3
\(0.2370 \, \text{g cm}^{-3}\)	Leading zero not significant 2370 all significant (trailing zeros after decimal)	2370	4
\(6.320 \, \text{J}\)	All digits significant Trailing zero after decimal significant	6.320	4
\(6.032 \, \text{N m}^{-2}\)	All digits significant Trailing zero after decimal significant	6.032	4
\(0.0006032 \, \text{m}^2\)	Leading zeros (0.0006) not significant 032 all significant	6032	4

Summary: (a) 1, (b) 3, (c) 4, (d) 4, (e) 4, (f) 4 significant figures

Verification Examples

Test Case	Rule Applied	Result
Why 0.007 = 1 sig fig?	Leading zeros never count	\(0.007 = 7 \times 10^{-3}\)
Why 0.2370 = 4 sig figs?	Trailing zeros after decimal count	Decimal place confirms precision
Why \(2.64 \times 10^{24}\) = 3 sig figs?	Only mantissa (2.64) counted	Exponent is exact number