Question

problem
which of the following shows the dimensional analysis to convert 4.5 dag into mg?
a. $4.5 dag\times\frac{1 mg}{10^{2} dag}=0.045 mg$
b. $4.5 dag\times\frac{10^{4} mg}{1 dag}=45,000 mg$
c. $4.5 dag\times\frac{1 mg}{10^{4} dag}=0.00045 mg$
d. $4.5 dag\times\frac{10^{2} mg}{1 dag}=450 mg$
e. $4.5 dag\times\frac{10^{3} mg}{1 dag}=4500 mg$
how many mm in 57.2 cm?
a. 572 mm
b. 0.0000572 mm
c. 0.572 mm
d. 0.0572 mm
e. 5.72 mm

Explanation:

Step1: Recall metric - prefix conversion

1 dag (decagram) = 10 g and 1 g = 1000 mg, so 1 dag=10×1000 mg = 10⁴ mg.

Step2: Perform dimensional - analysis

To convert 4.5 dag to mg, we multiply 4.5 dag by the conversion factor $\frac{10^{4}mg}{1 dag}$. So, $4.5 dag\times\frac{10^{4}mg}{1 dag}=45000 mg$.

Step3: Recall cm - to - mm conversion

1 cm = 10 mm.

Step4: Convert 57.2 cm to mm

Multiply 57.2 cm by the conversion factor $\frac{10mm}{1cm}$. So, $57.2 cm\times\frac{10mm}{1cm}=572 mm$.

Answer:

1. B. $4.5 dag\times\frac{10^{4}mg}{1 dag}=45000 mg$
2. A. 572 mm