Setting up a unit reprefix conversion

Question

(0.030 N/cm) x ? =? N/mm

Answer 1

To convert from N/cmN/cm to N/mmN/mm, you need to account for the difference in the units of length. Specifically, 1 cm equals 10 mm.

Conversion Steps:

1. Understand the Conversion Factor:
2. 1 N/cmN/cm is equivalent to 10 N/mmN/mm, because there are 10 mm in 1 cm.
3. Apply the Conversion:
4. To convert from N/cmN/cm to N/mmN/mm, multiply the value in N/cmN/cm by 10.

Given: 0.030 N/cm0.030 N/cm

Conversion: 0.030 N/cm×10=0.30 N/mm0.030 N/cm×10=0.30 N/mm

Answer:

0.030 N/cm=0.30 N/mm0.030 N/cm=0.30 N/mm

Answer 2

Use dimensional analysis.

0.030 N / cm x 1 cm / 10 mm = 0.0030 N/mm

Answer 3

Hi Alex,

Goal with these problems is to cancel out the unit you don't want and ultimately replace with the unit you do want. In this case, you want to get rid of cm. and replace with mm, retaining N. We don't know a direct conversion factor between cm. and mm., so we go to meters first. Thus:

0.030 N/cm. * (100 cm./1m) * (1m/1000mm.) = 0.003 N/mm.

Notice how both cm. and m. got cancelled. I hope this helps.