Question

Round off each of the following quantities to three significant figures:
A. ${\text{1}}{\text{.43 c}}{{\text{m}}^{\text{3}}}{\text{}}$
B. ${\text{458}} \times {\text{1}}{{\text{0}}^{\text{2}}}{\text{cm}}$
C. ${\text{643 c}}{{\text{m}}^{\text{2}}}$
D. ${\text{0}}{\text{.039 m}}$
E. ${\text{6}}{\text{.398}} \times {\text{1}}{{\text{0}}^{{\text{ - 3}}}}{\text{km}}$
F. ${\text{0}}{\text{.0179 g}}$
G. ${\text{79,000 m}}$
H. ${\text{42}}{\text{.150}}$
I. ${\text{649}}{\text{.85}}$
J. ${\text{23,642,000 mm}}$
K. ${\text{0}}{\text{.0041962 kg}}$

Answer 1

The rules for finding number of significant figures are, all non-zero digits are significant, zeroes in between other non-zero digits are significant, ending or final zero in the decimal portion only are significant, those digits which are non-zero are significant. It is an expression of precision.

Complete step by step answer:
Significant figures are the number of digits of value which have a meaningful power resolution of the measurement in chemistry. This finds application while finding analytical concentration. There are certain rules for determining the number of significant figures.
A. All non-zero digits are significant. 54678 contains five significant digits.
B. All zeros that come between any two non-zero digits are significant. For example, 28.005 contains six significant digits.
C. All zeros that are present on the right of a decimal point and on the left of a non-zero digit is not significant. For example, 0.00546 contains only three significant digits.
E. zeros on the right of a decimal point are significant, only if a non-zero digit does not follow. For example, 50.00 contains four significant digits.
F. All the zeros that are on the right of the last non-zero digit, after the decimal point, are significant. For example, 0.0098700 contains five significant digits.
G. If they come from a measurement, then all the zeros that are on the right of the last non-zero digit are significant. For example, 1570 m contains four significant digits.
Solution
A. ${\text{1}}{\text{.43 c}}{{\text{m}}^{\text{3}}}{\text{}}$: Here, no. significant figures are three
B. ${\text{458}} \times {\text{1}}{{\text{0}}^{\text{2}}}{\text{cm}}$: Here, no. significant figures are three
C. ${\text{643 c}}{{\text{m}}^{\text{2}}}$: Here, the no. of significant figures are three
D. ${\text{0}}{\text{.039 m}}$: Here, no. significant figures are three
E. ${\text{6}}{\text{.398}} \times {\text{1}}{{\text{0}}^{{\text{ - 3}}}}{\text{km}}$: Here, no. significant figures are three
F. ${\text{0}}{\text{.0179 g}}$: Here, no. significant figures are three
G. ${\text{79,000 m}}$: Here, ${\text{7}}{\text{.90}} \times {\text{1}}{{\text{0}}^4}{\text{ m}}$ no. significant figures are three
H. ${\text{42}}{\text{.150}}$: Here, ${\text{4}}{\text{.22}} \times {\text{1}}{{\text{0}}^4}$ , no. significant figures are three
I. ${\text{649}}{\text{.85}}$: Here, ${\text{6}}{\text{.50}} \times {\text{1}}{{\text{0}}^2}$ no. significant figures are three
J. ${\text{23,642,000 mm}}$: Here, ${\text{2}}{\text{.36}} \times {\text{1}}{{\text{0}}^7}{\text{ mm}}$,no. significant figures are three
K. ${\text{0}}{\text{.0041962 kg}}$: Here, ${\text{4}}{\text{.20}} \times {\text{1}}{{\text{0}}^{ - 3}}{\text{kg}}$ no. significant figures are three

Note: Precision is the closeness of two or more quantities to each other, it is the level of measurement that gives the exact result when repeated. Accuracy is the level of measurement that gives us true and consistent results Here, observed results agree with the true valves.