# Using Coins as Balance Weights

by Gregory King (gking@arserrc.gov)

Another option is to use a combination of coins. I weighed out an assortment of coins (U.S. pennies, nickels, dimes, and quarters) on a fairly sensitive scale (accurate to 0.01 gram) and got the following average masses (or weights, if you prefer):
```
penny = 2.67 gram (average of 7 coins)
nickel = 5.01 gram (average of 7 coins)
dime = 2.28 gram (average of 4 coins)
quarter = 5.66 gram (average of 8 coins)

```
Except for one badly-behaved penny with a mass of 3.08 gram, none of the coins' masses varied from the corresponding average value by more than 0.07 gram.

By playing around with various combinations of coins, I came up with the following:

```
0.2550 oz = 1 penny + 2 dimes
0.4984 oz = 1 nickel + 4 dimes
0.9982 oz = 5 quarters
1.9964 oz = 10 quarters

```
As you can see, these combinations of coins are good approximations for 1/4 oz, 1/2 oz, 1 oz, and 2 oz, respectively.

Here are the worst-case errors one could get using the above combinations, assuming a 0.07 gram error per coin and using Ken's approximation 1 hop pellet = 0.24 gram:

```
1/4 oz:  3 coins * 0.07 gram/coin = 0.21 gram = 0.9 hop pellet
1/2 oz:  5 coins * 0.07 gram/coin = 0.35 gram = 1.5 hop pellet
1 oz:  5 coins * 0.07 gram/coin = 0.35 gram = 1.5 hop pellet
2 oz: 10 coins * 0.07 gram/coin = 0.70 gram = 2.9 hop pellet

```
For statistical reasons, the errors are likely to be significantly less than these worst-case values.
Go to Ken Koupal's article on using brass rods as weights.