jwallach unit conversions metric conversions

1. Conversions with Metric Prefixes

2. Purpose
• This lesson has you combine your knowledge of unit conversions and
metric prefixes to do conversions with metric prefixes.

3. Conversions with metric prefixes – use
dimensional analysis
• Example
– Convert 1.3 x 105 μs (microseconds) to s (seconds).
• Plan – we know that the relationship between s and μs is
1 x 106μs = 1 s or 1 μs = 1 x 10-6s
• Solve – use the relationship that makes sense to you and solve
using dimensional analysis.
1.3 𝑥 105 𝜇𝑠 𝑥
1 𝑠
1 𝑥106 𝜇𝑠
= 0.13 𝑠

4. Conversions with metric prefixes
• Use dimensional analysis to make conversions.
– e.g. Convert 1.3 x 105 mm (millimeters) to km (kilometer).
• Plan – we will convert to the base unit (meters) first, then to km.
The relationships are: 1 x 103mm = 1m and 1 x 103m = 1 km
1.3 𝑥 105 𝑚𝑚 𝑥
1 𝑚
1 𝑥103 𝑚𝑚
𝑥
1 𝑘𝑚
1 𝑥103 𝑚
= 0.13 𝑘𝑚
• Note: We converted to the base unit m first, then to km. It could be done
as a single step but that will not be covered here.

5. Pause and Practice
• How many centiamps (cA) are equivalent to 124 nA (nanoamps)?
• A substance has a density of 2.3 g/mL. What is the density in kg/kL?

6. Pause and Practice Answers
• How many centiamps (cA) are equivalent to 124 nA (nanoamps)?
124 𝑛𝐴
1 𝐴
1 𝑥 109 𝑛𝐴
100 𝑐𝐴
1 𝐴
= 1.24 𝑥 10−5 𝑐𝐴
• A substance has a density of 2.3 g/mL. What is the density in kg/kL?
2.3
𝑔
𝑚𝐿
1 𝑘𝑔
1000 𝑔
1000 𝑚𝐿
1 𝐿
1000 𝐿
1 𝑘𝐿
= 2300
𝑘𝑔
𝑘𝐿

7. Now try the exercises