Measuring coins >

DENSITIES OF THE PHILIPPINE COINS

We use coins everyday. Many changes have been present in our national coins we use right now.

As a result, this has led to the different properties these coins have. After we measured the rice grains, which is a tedious task, we now moved on to measuring coins. Using calipers again, we sort of got a grip on how we should measure the coins. Measuring them were way, way easier than the rice grains. 

Anyway, as I've mentioned a while ago, our own coins have different properties, look: 

  Fig.1. Different Philippine coins. (source: images.delcampe.net)

It seems that as the value of the coin increases, it's diameter also increases. Of course, as we measure the properties we need to quantify, errors are present. That is, the "measurement" we will gather should always depend on the limitations of the devices we use for measuring plus our judgement on the reading. We (our group) were only able to measure 4 of the coins shown above (fig.1.), namely the:

 where:
          d = diameter                                   t = thickness
          d(in) = diameter of the inside        m = mass
                        

• 5-centavo coin: d=15.1 mm, d(in)  = 3.16 mm, t = 1.1 mm, m= 1.9g
• 25-centavo coin: d= 20 mm,  t = 1.6 mm, m= 3.8g
• 1-peso coin: d= 24 mm, t = 1.168 mm, m= 5.4g
• 5-peso coin: d= 27.16 mm,  t = 1.18 mm, m= 7.9g

Error propagation means that when one doesn't take account the uncertainty involved before using mathematical operations between his/her measured values (which are inherently uncertain),  the error will propagate. Basically, the computed value would have discrepancies from the expected value of measurement. It would probably be "away" by a matter of decimal places. Small, but the errors using operations might be big to be noticeable. To avoid these, one must continue the mathematical operations he/she started until he/she will reach the point where it is the final answer to all operations involved, rounding off with respect to the significant figures rule.