Significant Figures

1. All nonzero digits are significant. 
2. Sandwiched zeros are significant.
3. ONLY trailing zeros in a decimal number are significant. 
4. Leading zeros are NOT significant.
5. All numbers before x10 in scientific notation are significant. 

1. All nonzero digits are significant

• Ex: 120 = 2 sig figs

• Ex: 652,000 = 3 sig figs

• Ex: 40 = 1 sig figs

2. Sandwiched zeros are significant. 

• Ex: 205 = 3 sig figs

• Ex: 1006 = 4 sig figs

• Ex: 101,000 = 3 sig figs

3. Trailing zeros are not significant UNLESS in a decimal number. 

• Ex: 100 = 1 sig fig

• Ex: 100. = 3 sig fig

• Ex: 20.00 = 4 sig figs

4. Leading zeros are NOT significant. 

• Ex: 0.0025 = 2 sig figs

• Ex: 0.0003710 = 4 sig figs

• Ex: 0.0800 = 3 sig figs

5. All numbers before x10 in scientific notation are signigicant. 

• Ex: 3.0 x 10^3 = 2 sig figs

• Ex: 1.560 x 10^-2 = 4 sig figs

• Ex: 4 x 10^7 = 1 sig figs

Scientific Notation

How we write very big, and very small numbers! Also useful to show our significant figures. 

Steps to write in scientific notation:

• Step 1: Determine if we will need a negative or positive exponent. 

• Ex: 540,000 --> greater than 1, our exponent will be positive. 

• Ex: .0005400 --> less than 1, our exponent will be negative. 

Step 2: Determine the significant figures. 

• Ex: 540,000 = 2 sig figs

• Ex: 0.0005400 = 4 sig figs

Step 3: Count your placeholders. 

• You can determine the placeholders by the amount of spaces you will move your decimal. 

• Count down until you have a number between 1 and 9. 
  
  

• Ex: Number with positive exponent move to left

• 540,000 --> 5.40000 --> 5 spaces --> exponent will be positive 5. 
  
  

• Now write including only sig figs and x 10:

• 5.4 x 10^5

Step 3: Count your placeholders. 

• You can determine the placeholders by the amount of spaces you will move your decimal. 

• Count down until you have a number between 1 and 9. 
  
  

• Ex: Number with negative exponent move to right

• 0.0005400 --> 005.400 --> 4 spaces --> exponent will be negative 4. 
  
  

• Now write including only sig figs and x 10:

• 5.400 x 10^-4

Step 1: Writing in Standard (expanded) form

• Determine if you have a number greater 1 --> positive exponent

• Ex: 4.20 x 10^5 

• Determine if your number issmaller than 1 --> negative exponent

• Ex: 4.20 x 10^-3

Step 2: Direction you need to move decimal

• Positive exponent = right

• Negative exponent = left
  
  
  

Step 3: Move the decimal the same number as the exponent. 

• Ex: 4.20 x 10^5 = 420000 

• Ex: 4.20 x 10^-3 = .00420 

• *Notice that whether the decimal moved left or right any blank spaces were filled with zeros. 

Metric Conversions

We can easily convert from one unit in metric to another by moving the decimal point. 

Base Units:

Meters - m
Liters - L
Grams - g

Using the chart to convert

Find your starting unit

Density

Measurement of mass per volume. 

Tip: You can use units to help you identify the variable given in a problem. 

• mass --> g 

• volume --> mL or L or cm^3

• density --> g/mL or g/L or g/cm^3

Percent Error

Helps us compare our measured values to the true values. 

Percent Error

True value = actual, known, accepted value