Question

What is the solution to the problem expressed to the correct number of significant figures?

Answer 1

Answer :  The correct answer will be $8.79\times 10^3$

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 multiplication and division is :

The least number of significant figures in any number of the problem determines the number of significant figures in the answer.

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.

The given expression is:

$(102900\div 12)+(170\times 1.27)$

$\Rightarrow 8575+215.9$

$\Rightarrow 8790.9$

$\Rightarrow 8.79\times 10^3$

In the given expression, 102900 has 6 significant figures, 12 has 2 significant figures, 170 has 3 significant figures and 1.27 has 3 significant figures. From this we conclude that 3 is the least significant figures in this problem. So, the answer should be in 3 significant figures.

Thus, the answer will be $8.79\times 10^3$

Answer 2

(102 900 ÷ 12) + (170 × 1.27) = 8800

Step 1. Evaluate the expressions inside the parentheses (PEMDAS)

102 900 ÷ 12 = 8575

170 × 1.27 = 215.9

In multiplication and division problems, your answer can have no more significant figures than the number with the fewest significant figures.

Thus, the underlined digits are not significant, but we keep them in our calculator to avoid roundoff error.

Step 2. Do the addition (PEMDAS).

   8575

+    215.9

= 8790.9

Everything that you add to an insignificant digit gives an insignificant digit as an answer.

Thus, the underlined digits are not significant.

We must drop them and round up the answer to 8800.