An Introduction to Significant Figures

When you complete the math section of the SAT, you will see some questions requiring you to round your answer to a certain number of significant figures.

If you don’t know what significant figures are, you may very well miss these questions, even if you have completed the right calculations to solve the math problem.

To do well on standardized tests like the SAT or in your advanced math classes, it is important that you know the definition of significant figures and the rules for determining significant figures.

If this seems daunting, don’t worry. Prep Expert has your back. This guide will help you understand everything you need to know about significant figures:

What are significant figures?

Significant figures, also known as significant digits, are used to determine which numbers in a set of digits are important. They make sure that your value is meaningful and add precision to a number.

For example, the number 15.465 has five significant figures, and each of these values are critical for maintaining the number’s accuracy.

If a swimmer completes a heat in 15.465 seconds, those tiny thousandths of a second are essential to know because they can determine whether or not the swimmer was faster than the other swimmers in their heat. Someone who finishes in 15.465 seconds will place higher than someone who finishes in 15.466 seconds, which is why each figure in this number is significant.

How do I determine significant figures?

To fully understand the meaning of significant figures, you will need to know the rules for determining significant figures.

Here is a list of the rules for significant figures you’ll need to know:

• Any non-zero number is significant. The number 145 has three significant figures. The number 21.4 also has three significant figures. The number 45698392839 has eleven significant figures.
• Any zeros that occur between significant figures are significant. If there are zeros sandwiched  between two significant figures, they are considered significant, too. The number 2409 has four significant figures. The number 301.7 has four significant figures. 
• Leading zeros are not significant figures. If there is a zero to the left of a significant number, but to the right of a number that isn’t significant, that zero is not significant. The number 0.34 only has two significant figures. The number 0.0048 has two significant figures.
• Trailing zeros in numbers with decimal points are significant figures. If there are zeros that come to the right of a significant figure in a number with a decimal point, the zeros are significant. For instance, the number 45.00 has four significant figures.
• Trailing zeros in numbers without decimal points are not significant figures. The number 380 has two significant figures. The number 10540 has four significant figures.
• Trailing zeros after a decimal point following a non-zero digit are significant. The number 0.0093400 has five significant figures. The number 0.0123000 has six significant figures.
• All the numbers in a specific measurement or unit are significant. If you have a story problem where the solution is 450 miles, there are three significant figures. So while 210 has two significant figures, 210 feet has three significant figures.

Examples of significant figures

If you’re having trouble determining significant figures, here are some examples to help you get a better grasp on this concept.

Number	Total number of significant figures
0.01	1
35	2
7890	3
4008	4
3812.2	5
4.308	4
21.3	3
0.33	2
2	1

How do I round significant figures?

If you see a math problem that asks you to round a number to a specific number of significant figures, you’ll need to make sure you’re keeping the rules above in mind. However, you’ll also need to consider two more rules:

• If a value of the digit you need to round is greater than or equal to 5, you will add a digit to the number to the left of this number.
• If a value of the digit you need to round is less than 5, you will keep the digit to the left the same.

Here is an example:

Say you solve a math problem and get 0.0184 as your answer, but you are asked to round your answer to the nearest two significant figures.

The number 0.0184 has three significant figures (1, 8, and 4). To round this answer correctly, it means you will need to round the third significant figure so that you end up with only two significant figures instead.

Since the number you need to round in this example, 4, is less than 5, you will not need to change the digit in front of it. This means your final answer will be 0.018.

Here is another example:

Say you are solving a math problem and get 0.0185 as your answer, and you are asked to round your answer to the nearest two significant figures.

As in the previous example, the number 0.0185 has three significant figures. This time, however, the significant figures are 1,8, and 5. Since the number you’ll need to round is equal to five, you need to add a digit to the value in front of it. This means that your final answer will be 0.019.

Understanding significant figures

While this guide is a great starting point, there are more steps you can take to further your understanding of significant figures.

Here are a few steps you should take to get a good handle on this concept:

Practice

One of the best ways to become familiar with significant figures is to practice determining the number of significant figures in a value and to practice rounding significant figures as well.

Try determining the number of significant figures in the following set of digits:

A.) 670

B.) 54.00

C.) 1024

D.) 0.043

E.) 21.03

Before you look at the answers below, try to figure out the number of significant figures for A-E on your own.

When you’re ready for the answers, you should have: A= 2, B= 4, C= 4, D= 2, and E= 4

You can also practice rounding significant figures using the examples below:

1. Round 0.0467 to the nearest two significant figures
2. Round 41.4 to the nearest two significant figures
3. Round 0.191 to the nearest two significant figures

When you’ve figured out the answers, you should have: A= 0.047, B= 41, and C= 0.19

Remember, practice makes perfect. The more time you spend working on mastering this concept, the easier it will be.

Work with a private tutor

If significant figures or any other math concept seems to go over your head, working with a private math tutor can help. A private tutor can help you practice and develop strategies to make it easier for you to remember the rules for determining and rounding significant figures.

Start working with a private tutor through Prep Expert today when you visit our website.