Unit Conversions of Force: How to Convert Between Different Units of Force?

[kokofaen]

TL;DR Summary

Kg to dg, m to cm and s to ms

Hello.
Im studying for an exam and came across this simple unit conversion question but I haven't done something like this in a long time! I understand the conversions of each unit individually but get a bit stuck combining them. This is the question:

A force of 100 N is exerted on an object with the base units of Kg∙m∙(s)^-2
Express this in dg∙cm∙(ms)^−2

The answer:
100 dg∙cm∙(ms)^−2 = 1.0 x 10^2(dg∙cm∙(ms)^−2)

Could someone please explain why the converted answer is still simply 100 when the units have been converted to different degrees (e.g. 1kg =10,000 dg vs 1m =100cm)? Thank you!

 

[PeroK]

You also have to convert seconds to milliseconds.

 

[berkeman]

Welcome to PF.

the units have been converted to different degrees

What is "dg" as a unit? Degrees? Decigrams? Something else?

Assuming from your equations that dg is decigrams, how many decigrams per kilogram? Remember that when converting units, one of the best ways is to just multiply through by terms that are "1" in value, but have both sets of units (the old ones and the new ones) expressed as a fraction. For example, if you want to convert some number of seconds to hours, you would do this:
$$7200 [seconds] = 7200 [seconds] \times 1 = 7200 [seconds] \frac{1 [hour]}{3600 [seconds]} = 2 [hour]$$

 

[kokofaen]

What is "dg" as a unit? Degrees? Decigrams? Something else?

Assuming from your equations that dg is decigrams, how many decigrams per kilogram? Remember that when converting units, one of the best ways is to just multiply through by terms that are "1" in value, but have both sets of units (the old ones and the new ones) expressed as a fraction. For example, if you want to convert some number of seconds to hours, you would do this:
$$7200 [seconds] = 7200 [seconds] \times 1 = 7200 [seconds] \frac{1 [hour]}{3600 [seconds]} = 2 [hour]$$

Hi, yes thank you for that.
The unit is decigrams.

So based on what you've said, would the working for this equation look like this:
1 kg = 10,000 dg
1 m = 100 cm
1 s = 1000 ms

Also could I clarify that the reason the seconds and milliseconds are the reciprocal of the other units (which have the units converting TO as the numerator and FROM as the denominator) is because the units for newtowns are S^-2 or ms^-2 respectively?

 

[PeroK]

Ĺ

Hi, yes thank you for that.
The unit is decigrams.

So based on what you've said, would the working for this equation look like this:
1 kg = 10,000 dg
1 m = 100 cm
1 s = 1000 ms

View attachment 337223

Also could I clarify that the reason the seconds and milliseconds are the reciprocal of the other units (which have the units converting TO as the numerator and FROM as the denominator) is because the units for newtowns are S^-2 or ms^-2 respectively?

If a particle moves at $1m/s$, then that is only $0.001 m$ per millisecond. Or $1$ millimeter per millisecond. $1 m/s$ is certainly not the same as $1km$ per millisecond.