Question

express the following sum to appropriate number of significant figures:
a.2.3× 103 ML+4.22×104ML+9.04×103ML+8.71×105ML
b.319.5g - 20460g -0.0639 g -45.645g -4.173g​

Answer 1

Answer :

(a) The answer will be $9.2\times 10^5mL$

(b) The answer will be $-20190g$

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.

The rule apply for the addition and subtraction is :

The least precise number present after the decimal point determines the number of significant figures in the answer.

(a) The sum of the measured values are,

$(2.3\times 10^3mL)+(4.22\times 10^4mL)+(9.04\times 10^3mL)+(8.71\times 10^5mL)$

$\Rightarrow 9.2\times 10^5mL$

In the given expression, $(2.3\times 10^3)$ has 2 significant figures, $(4.22\times 10^4)$ has 3 significant figures, $(9.04\times 10^3)$ has 3 significant figures and $(8.71\times 10^5)$ has 3 significant figures. From this we conclude that least precise number present after the decimal point is 1.

Thus, the answer will be $9.2\times 10^5mL$

(a) The sum of the measured values are,

$319.5g-20460g-0.0639g-45.645g-4.173g​$

$\Rightarrow -20190g$

In the given expression, 319.5 has 4 significant figures, 20460 has 5 significant figures, 0.0639 has 3 significant figures, 45.645 has 5 significant figures and 4.173 has 4 significant figures. From this we conclude that least precise number present after the decimal point is 0.

Thus, the answer will be $-20190g$