# How are decimals used to find significant figures?

Dec 3, 2016

Decimals determine whether or not zeroes count as significant figures.

#### Explanation:

Just to make sure this is covered: All nonzero number (any number from 1-9) count as a significant figure.

Trailing Zeroes are really the only case where decimal point can affect the number of significant figures, but I'll cover captive and leading zeroes because some cases of existent decimal points can be confusing.

Trailing Zero:

Trailing Zeroes make all zeroes after a nonzero significant, given a decimal point is present. For example,

1.00 has 3 significant figures, as there is a decimal point present and two zeroes following a nonzero digit.

650.0 has 4 significant figures, as there is a decimal point present and two zeroes following a nonzero digit.

.500 has 3 significant figures, as there is a decimal point present and two zeroes following the nonzero.

400 has 1 significant figure, as there is no decimal point present, thus making the '4' the only significant figure.

As you can see, the position of the decimal point does not matter, as long as there are zeroes following a nonzero digit.

Captive Zero:

Captive Zeroes make zeroes in between two nonzero digits significant. I like to think about this as the zero being held 'captive' by the nonzero digits. For example,

10.01 has 4 significant figures, as the two zeroes are in between nonzero digits.

4.01 has 3 significant figures, as the zero is in between nonzero digits.

102.03 has 5 significant figures, as each zero is in between nonzero digits.