SIGNIFICANT FIGURES

Sometimes, we have to round numbers up so as to approximate the values especially in cases where the numbers are very huge  or very small. One way of doing that is by leaving them in significant figures. 

By the end of this article, you'll be able to answer the following questions. 

1. What are significant figures?

2. Can you give an example of a number with 3 significant figures?

3. How do you identify significant figures in a number?

4. What about numbers with zeros? Are they always significant?

Lets dive into it. 

Understanding Significant Figures

1. What are significant figures?

• Significant figures are the digits in a number that are reliable and meaningful.

2. How do you identify significant figures in a number?
• All non-zero digits are significant. 
• Zeros between non-zero digits are significant.
•  Leading zeros (zeros before the first non-zero digit) in decimals numbers are not significant but they are place holders. i.e They are written so not to change the value of the number. This means 0.02 has 1sf, and 0.2 also is 1sf. 0.21 is 2sf.
•  Leading zeros (zeros before the first non-zero digit) in whole numbers are not significant and must be removed. ie. 013 is the same as 13 and it has 2sf.  
•  Trailing zeros (zeros after the last non-zero digit) are significant only if the number contains a decimal point. This means 2.0 has 2sf but 20 has 1 sf. 

3. Rounding to a Specific Number of Significant Figures

1. Round the following numbers to 2 significant figures:

• 34.56

From the first rule, we can say that 34.56 has 4 sf. so leaving it at 2sf, we start from the left. i.e the number 3 and 4 are the first two significant figures, but the next number is a 5 so we add one to the last significant figure to form 35

• 1234

This number has 4 significant figures so we choose the first two and replace the others with zeros. (Remember trailing zeros in whole numbers are just place holders) so we ge 1200. 

• 0.00567

This number has 3sf. we choose the first two and add one to it since the third number is more than 4. we will have 0.0057.

Now try your hands on these questions. 

Round the following numbers to 3 significant figures:

• 78.901
• 0.12345
• 50

If your answers are 78.9, 0.123 and 50.0, then you're right. 

Assignment

1. In a science experiment, you measure the length of a piece of string to be 12.345 cm. If the experiment only requires accuracy to the nearest centimeter, what should you round the measurement to?
2. A scientist measures the mass of a sample to be 0.004567 g. If the instrument can only measure to the nearest 0.001 g, what should the mass be reported as?
3. A calculator shows the result of a calculation as 3.141592654. If you need to report the answer to 3 significant figures, what would it be?

Make sure to send your answers to my email stakhanovite91@gmail.com and I will get back to you.