Question 5.6.5: Significant digits Assume that the given numbers are measure...
Significant digits
Assume that the given numbers are measurements. Perform each computation, and give the answer with the appropriate number of significant digits.
a. sin(123.4°) b. \frac{\cos \left(3^{\circ}\right)}{\sin \left(1.9^{\circ}\right)} c. 544 \cdot \sin \left(25^{\circ}\right)
.a. Since 123.4° has four significant digits, we round the calculator value to four decimal places. So sin(123.4°) ≈ 0.8348.
.b. Since the least number of significant digits in 3° and 1.9° is one, round the value obtained on a calculator to one significant digit:
\frac{\cos \left(3^{\circ}\right)}{\sin \left(1.9^{\circ}\right)} \approx 3 \times 10^{1} (to the nearest ten)
.c. The least number of significant digits in 544 and 25° is two. So
544 \cdot \sin \left(25^{\circ}\right) \approx 230 (to the nearest ten).
In scientific notation, 544 \cdot \sin \left(25^{\circ}\right) \approx 2.3 \times 10^{2}.