Question

name: perform the following operations. make sure that your answers have the correct number of significant figures. 35. 4.15 cm x 1.8 cm = 36. 13.00 m - 0.54 m = 37. 3.14159 x 4.0 = 38. 43.2 x 3.00 = 39. 44.01 + 13.4 + 87.40 = 40. 71.6 + 45.32 - 8 = 41. express a length of 16.45 m in centimeter. 42. express a length of 16.45 m in kilometers. 43. 1.2 l equals how many ml? 44. 10.5 g to kg. 45. why is the temperature at which a density is measured usually specified?

Explanation:

Step1: Perform subtraction

$13.00 - 0.54=12.46$ m. Since the least number of decimal - places in the values being subtracted is 2, the answer is $12.46$ m.

Step2: Perform multiplication

$3.14159\times4.0 = 12.56636$. The number $4.0$ has 2 significant figures, so the answer rounded to 2 significant figures is $13$.

Step3: Perform multiplication

$43.2\times3.00 = 129.6$. The number $43.2$ has 3 significant figures and $3.00$ has 3 significant figures, so the answer is $130$ (rounded to 3 significant figures).

Step4: Perform addition

$44.01+13.4 + 87.40=144.81$. The number $13.4$ has the least number of decimal - places (1 decimal place), so the answer is $144.8$.

Step5: Perform addition and subtraction

$71.6+45.32 - 8=108.92$. The number $8$ has no decimal places, so the answer is $109$.

Step6: Convert meters to centimeters

Since $1$ m = $100$ cm, then $16.45$ m $\times100 = 1645$ cm.

Step7: Convert meters to kilometers

Since $1$ km = $1000$ m, then $16.45$ m $\div1000=0.01645$ km.

Step8: Convert liters to milliliters

Since $1$ L = $1000$ ml, then $1.2$ L $\times1000 = 1200$ ml.

Step9: Convert grams to kilograms

Since $1$ kg = $1000$ g, then $10.5$ g $\div1000 = 0.0105$ kg.

Step10: Explain density and temperature

Density is mass per unit volume. The volume of a substance can change with temperature (most substances expand or contract with temperature changes). Since density is $
ho=\frac{m}{V}$, and $V$ can change with temperature, the temperature at which density is measured must be specified to accurately define the density value.

Answer:

1. $12.46$ m
2. $13$
3. $130$
4. $144.8$
5. $109$
6. $1645$ cm
7. $0.01645$ km
8. $1200$ ml
9. $0.0105$ kg
10. The volume of a substance can change with temperature, and since density is mass per unit volume, temperature must be specified to accurately define density.