Question

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

Answer 1

(a) There are 3 significant figures.

(b) There are 1 significant figures.

(c) There are 7 significant figures.

(d) There are 6 significant figures.

(e) There are 3 significant figures.

(f) There are 3 significant figures.

(g) There are 4 significant figures.

Explanation :

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:

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

(a) 38.7 g

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

(b)
`2* 10^(18)m`

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)
`9.74150* 10^(-4)J`

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

(e)
`0.0613cm^3`

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.