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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
Expert Contributor
Wiley Iverstine

Wiley Iverstine holds master’s degree in natural science from Louisiana State University and spent 27 years teaching DE, AP, Regular & Honors Chemistry/Physics.

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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Additional Activities

The Why of Significant Digits

The problem for most students to develop the use of significant digits is that it is hard to understand the "why" of significant digits. To deepen one's understanding of the application of a subject one must not only understand what to do but why you're doing it. The why of significant digits is built on the idea of why we use math in science. Science does not actually just use math but the function of math as a tool. Math is a language. Languages are meant to communicate. When scientists use math they are communicating ideas about objects. When we teach math in a classroom we just practice the manipulation of numbers. In science, we're not just manipulating numbers but we're communicating ideas. A good example is when a scientist collects data on an object such as its weight, height, the pressure within a tank, temperature in the air. Understand these are not numbers but actually measurements that communicate information about the object to help us better understand the object, the material that it's made of and how it interacts with the environment that surrounds it. To gain this data we must use measuring devices and the measuring devices must communicate the information to us. These measuring devices have a certain degree of ability by which they can convey information. Because of this limited ability, we say that a measuring device can only portray a limited degree of understanding. The way to convey this limited ability is by digits that we call significant. So by looking at a measurement, we know how limited the measuring device was in its ability to communicate the measurement.

Significant Figures Activity

To practice this idea and enhance these concepts in a real-world sense, assign your students to walk through their house and catalog at least five measuring devices within the room i.e. clocks, thermostats, the temperature gauge on an oven, speed settings on a blender, etc. Then try and determine how many significant figures a normal reading would provide. Have your students take pictures of each of the examples and discuss them with the class to apply the rules of significant figures.

As an example, think of a digital clock that displays 7:54. We know that this communicates to us that the time of day is in the 19th hour of 24 (7 past 12 noon) plus 54 of 60 minutes. These three digits are significant and can be known to that degree but the clock is limited in that it does not communicate to any degree beyond that. We do not know how many seconds or milliseconds have passed since the time was exactly 54 minutes past the 19th hour.

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