Significant Digits or Figures

Significant Digits or Figures

The significant digits of a number are the digits that have meaning or contribute to the value of the number. Sometimes they are also called significant figures.

Which digits are significant?

There are some basic rules that tell you which digits in a number are significant:

• All non-zero digits are significant
• Any zeros between significant digits are also significant
• Trailing zeros to the right of a decimal point are significant

Which digits aren't significant?

The only digits that aren't significant are zeros that are acting only as place holders in a number. These are:

• Trailing zeros to the left of the decimal point (note: these zeros may or may not be significant)
• Leading zeros to the right of the decimal point

Counting Significant Figures

How many significant figures are there in the following numbers?

1) 10.0075

There are 6 significant digits. The zeros are all between significant digits.

2) 10.007500

There are 8 significant digits. In this case the trailing zeros are to the right of the decimal point.

3) 0.0075

There are 2 significant digits. The zeros shown are only place holders.

4) 5000

There is only 1 significant digit. The zeros are place holders. Note: It could be that some of the zeros are significant in certain cases.

5) 5000.00

There are 6 significant digits. The zeros to the right of the decimal point are significant because they are trailing zeros to the right of a decimal point. The zeros to the right of the 5 are significant because they are between significant digits.

Why use significant figures?

Significant figures are often used for science and measurements. They are a way to describe how accurate measurements are. Some ways of measuring are more accurate than others.

For example, let's imagine you had two scales, one that was accurate to the nearest gram and another that was accurate to the nearest one hundredth of a gram. If they both had a measurement of 3 grams, this number would mean different things. The first measurement you would record as just 3 grams, because you only know that the measurement is accurate to 1 gram. The second measurement you could record as 3.00 grams. This says that the measurement was accurate to the hundredths place. These extra significant figures help to record how accurate the measurement was.

Is there such thing as an exact number?

Yes, exact numbers have an infinite number of significant figures. There are certain measurements and numbers that we know with certainty. They include numbers like how many feet are in a yard or how many pages are in a book.