Shayla: If the Bible is infallible, why does it get the value of pi wrong in its description of Solomon’s sea of cast metal?

Midrash:

1 Kings 7:23. The charge is that the Bible teaches that pi (the ratio of the circumference of a circle to its diameter) is only 3 when it ought to have been given as 3.1416. Solomon is charged with saying that the circumference of a 10-cubit diameter circle is only 30 cubits when it should be 31.416 cubits. However, it is quite important that the scientist be accurate in his statement of the precision of measurements. To assure this, he uses a conventional technique called “significant figures.” It is only correct to state a measurement to the number of significant figures warranted by the accuracy of the measurement. Thus, if the number is stated as 10 cubits, it is accurate only to two significant figures and might actually be anywhere between 9.5 cubits and 10.5 cubits. If the writer had said it was 10.0 cubits, it would supposedly be accurate to three significant figures.

Similarly, the 30-cubit circumference is accurate only to two significant figures, and might really be anything from 29.5 cubits to 30.5 cubits. It served no purpose to specify the dimensions to a higher degree of precision than two significant figures, and so the writer simply rounded them off.

For example, say the actual measurement of the diameter gave 9.67 cubits, accurate to three significant figures. 3.14 should then multiply this, which is pi to the third significant figure. The result is 30.4 cubits, to the third significant figure. There cannot properly be more significant figures in a product than in any of its factors. It may not even be this accurate (if the diameter had been 9.665 cubits, multiplying by 3.14 would give 30.3 cubits instead of 30.4). It is quite common, for this reason, to retain one more significant figure in each factor than is needed in the product, which is then rounded off to one less significant figure than the factors have.

It would be perfectly proper and scientific, therefore, to round off the diameter of 9.67 cubits and the circumference of 30.4 cubits to 10 cubits and 30 cubits, respectively. Therefore, the writer of 1 Kings was actually more scientific than his critics.