Significant Figures and Rounding

Accuracy -  how close the measurement is compared to the actual value
Precision - to what value does measuring the same object under the same conditions show the same result

An instrument can be very precise but not accurate
Example- a ruler could have precision down to the milimeter but if the ruler does not have to necessarily be accurate with its measurements.

Significant Figures or Meaningful Digits

• The more significant figures a measurement has, the more precise the measurement is
• The last significant digit in the measurement is uncertain
• All of the other significant digits are certain
• Significant digit contains all the certain digits and only the FIRST uncertain digit
• Any zero between a decimal and a significant digit do not count if the number is smaller than 1
• Zeros after significant digits count if there is a decimal
• Zeros between two significant digits also count

This example shows when zeros do not count as significant digits

•  0.00023
• Only 2 and 3 count as significant digits
• The four zeros in front DO NOT count  

These zeros count as significant digits

• 3000 = 1 significant digit
• 1.01 = 3 significant digits
• 1.1000 = 5 significant digits

To help you understand scientific notation better, here is a QUIZ on it:

Exact Numbers/ Rounding

Some numbers are exact and so are not to be rounded

• The number of people in your family
• Amount of pencils in a pencil case
• A dozen = 12

Rounding:
When Rounding, you will round up when the digit is five or up and you will round down if digit is 4 and under
HOWEVER: if the digit 5 is the last digit, then you would round to the nearest even number (zeros after the five follow this rule too)

Math and Significant Figures
When adding or subtracting significant figures, round the answer to the least amount of decimal digits shown in the question.

Example:

  23000

  15600

+33120

  71720

However, because there are certain digits that you are unsure of, 71720 is NOT your final answer. The question would actually be something like this:

  23???

  156??

+3312?

  71???

Since we know that hundreds place is a 7, we would round our answer up and so the answer to this addition question, with consideration of significant figures would be: 72000

Multiply and Dividing

When multiply or dividing, we round the answer to the least amount of significant figures present in the question.

Example:

135x1 = 100

This is because 1 only has one significant digit and so when the product is 135, we round it so it would only have 1 significant digit (the hundreds) and so it becomes 100.

23.56/1.12 = 21.0

Since 1.12 only has three significant figures, the answer to this question will only have 3 significant figures as well.