What Are Significant Digits? - Definition, Rules & Examples

What Are Significant Digits? - Definition, Rules & Examples
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  • 0:01 What Are Significant Digits?
  • 1:30 Counting Significant Digits
  • 8:20 Lesson Summary
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Lesson Transcript
Instructor: Ryan Hultzman
In this lesson, you will learn about significant digits and the rules used to identify the number of digits that are significant in a figure. We will also discuss the relevance of significant figures in our experiences.

What Are Significant Digits?

If I offered you some money between $1,000 and $10,000, how much would you want? I'm sure when you are considering your answer, it is the first digit that is important to you because it tells you exactly how many thousand you would get.

That's an example of how significant digits work, it gives meaning to certain digits in a number. Scientists use significant digits to help them with more precise information about measurement and other numeric data. These digits also help them with rounding very large or very small numbers.

Significant digits are certain digits that have significance or meaning and give more precise details about the value of the number. If in our opening scenario, I offered you $2,000, the 2 in 2000 is significant because it tells you exactly how many thousands.

Let's say two people ran a race. Runner 1 took 30.01 seconds, and runner 2 took 30.02 seconds. Who would win the race? Obviously, runner 1 because he took less time. All those numbers are significant because we need them all to tell us exactly who won the race.

Counting Significant Digits

So, how do we decide what is significant? To find the number of significant digits in a number, we have to literally count each individual digit. For example, one hundred and forty is written as 140. It has a 1, a 4 and a 0. It has 3 digits. But not all of those digits are significant. In order to find out which ones are significant, we have to follow some rules.

Rule 1: Every Non-Zero Digit Is Significant

Remember that non-zero digits, are numbers other than zero, numbers 1 through 9. Anywhere you see a digit that is not zero, count it; it is significant.

Let's look at some examples:

  • 456 has 3 significant digits
  • 68.29 has 4 significant digits

All the other rules have to do with the number zero. Sometimes zero is not significant, and sometimes it is. In order to remember the rules about zero, let's pretend that two adults and a child are walking down the street. The adults are like the non-zero digits, and the child would be zero.

Rule 2: Zeros Between Non-Zero Digits Are Always Significant

In terms of our adults and child walking down the street, it's always okay for the child to walk between two adults.

Let's look at a few examples:

  • 5,609 has 4 significant digits.
  • 700.0879 has 7 significant digits.

Rule 3: Zeros Before Non-Zero Digits Are Never Significant

These are called leading zeros. That means if a number begins with zero, as in decimals, they are not significant. This is just like how it's never okay for the child to be far ahead of the adults walking by himself.

Notice that 8 * (1/1000) = 0.008 and 37 * (1/1000) = 0.0037. We know that we are multiplying by 1/1000; that doesn't change, but when the value in front changes the result changes; therefore, only that part is significant.

Let's look at a few examples:

  • 0.067 has 2 significant digits
  • 0.000008 has 1 significant digit
  • 098 has 2 significant digits

Rule 4: Zeros Behind Non-Zero Digits Are Sometimes Significant.

We have two cases for rule 4. Notice that zeros behind non-zero digits are called trailing zeros. Think of it this way, it's sometimes safe for the child to be behind (or trail) the adults, just in the event of danger.

Case 1

When there is no decimal, zeros behind non-zero digits are not significant.

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