How many significant figures are contained in each of the following measurements? (a) 38.7 g (b) 2 × 1018 m (c) 3,486,002 kg (d) 9.74150 × 10−4 J (e) 0.0613 cm3 (f) 17.0 kg (g) 0.01400 g/mL

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

Rules for significant figures:

Digits from 1 to 9 are always significant and have infinite number of significant figures.
All non-zero numbers are always significant. For example: 654, 6.54 and 65.4 all have three significant figures.
All zero’s between integers are always significant. For example: 5005, 5.005 and 50.05 all have four significant figures.
All zero’s preceding the first integers are never significant. For example: 0.0078 has two significant figures.
All zero’s after the decimal point are always significant. For example: 4.500, 45.00 and 450.0 all have four significant figures.
All zeroes used solely for spacing the decimal point are not significant. For example : 8000 has one significant figure.
The exponential digits present in scientific notation are not significant, only decimal digits the significant. For example: [tex]1.9\times 10^{9}[/tex] has 2 significant figures (1 and 9).

(a) 38.7 g

According to the 2nd rule, there are 3 significant figures.

(b) [tex]2\times 10^{18}m[/tex]

According to the 7th rule, there are 1 significant figures.

(c) 3,486,002 kg

According to the 2nd rule, there are 7 significant figures.

(d) [tex]9.74150\times 10^{-4}J[/tex]

According to the 7th rule, there are 6 significant figures.

(e) [tex]0.0613cm^3[/tex]

According to the 4th rule, there are 3 significant figures.

(f) 17.0 kg

According to the 5th rule, there are 3 significant figures.

(g) 0.01400 g/ml

According to the 4th rule, there are 4 significant figures.