## Significant Digits

“Significant digits” is a fancy way of describing the precision of a given value. If the value you are converting has four digits, the result should have four digits. Significant digits are important when converting values, because conversion involves multiplying by a conversion factor and then rounding. (See “Rounding”.)

Results: When multiplying or dividing, the result should not have more significant digits than the factor with the fewest significant digits. (The rule for addition and subtraction is a little different, but will rarely, if ever, come up in our work.) DO NOT round off factors before converting; convert and then round off. (See “Rounding”)

Zero as Number vs. Zero as Placeholder: Sometimes zero represents a numerical value;* i.e.*, “1000” means exactly one thousand. Zero can also indicate an order of magnitude or degree of precision; *i.e.*, “1.000” is numerically equal to “1”, but the “1.000” indicates that the quantity is measured to four significant digits. It is important to include placeholder zeroes in the significant digits because they imply the degree of precision in the quantity.

## Rounding

Determine the appropriate number of significant digits first. Then round off if necessary. (Do the calculation before rounding.)

When rounding to fewer digits than the total available, proceed as follows:

- If the first digit discarded is less than 5, do not change the last digit retained. For example, 3.4632 rounded to four digits is 3.463; rounded to three digits is 3.46.
- If the first digit discarded is greater than 5, increase the last digit retained by one. For example, 8.3765 rounded to four digits is 8.377; rounded to three digits is 3.78.
- If the first digit discarded is exactly five, followed only by zeroes, round the last digit retained UP if it is an ODD number, but make no change if it is an EVEN number. For example, 4.365 rounded to three digits is 4.36, but 4.355 rounded to three digits is also 4.36.
- It is important to remember the relative magnitude of units of measure when converting. For example, a measurement to the nearest 1/16 inch is properly converted to the nearest millimeter because those two units are of the same magnitude.
- Keep in mind that that decimalizing inch-pound units will affect the number of significant digits; i.e., 1-3/16 inch = 1.1875, for a total of five significant digits.

Be practical when rounding:

- It is important to remember the relative magnitude of units of measure when converting. For example, a measurement to the nearest 1/16 inch is properly converted to the nearest millimeter because those two units are of the same magnitude.
- Keep in mind that that decimalizing inch-pound units will affect the number of significant digits; i.e., 1-3/16 inch = 1.1875, for a total of five significant digits.