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

(a). The given quantity is 0.007 m².

If the number is less than one, then all zeros on the right of the decimal point (but left to the first non-zero) are insignificant. This means that here, two zeros after the decimal are not significant. Hence, only 7 is a significant figure in this quantity.

(b). The given quantity is 2.64 × 10²⁴ kg.

Here, the power of 10 is irrelevant for the determination of significant figures. Hence, all digits i.e., 2, 6 and 4 are significant figures.

(c). The given quantity is 0.2370 g cm^–3.

For a number with decimals, the trailing zeroes are significant. Hence, besides digits 2, 3 and 7, 0 that appears after the decimal point is also a significant figure.

(d). The given quantity is 6.320 J.

For a number with decimals, the trailing zeroes are significant. Hence, all four digits appearing in the given quantity are significant figures.

(e). The given quantity is 6.032 Nm^–2.

All zeroes between two non-zero digits are always significant

f). The given quantity is 0.0006032 m² .

If the number is less than one, then the zeroes on the right of the decimal point (but left to the first non-zero) are insignificant. Hence, all three zeroes appearing before 6 are not significant figures. All zeros between two non-zero digits are always significant. Hence, the remaining four digits are significant figures.