Approximations & Error
Skill Checklist
Track your progress across all skills in your objective. Mark your confidence level and identify areas to focus on.
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Track your progress:
Don't know
Working on it
Confident
📖 = included in formula booklet • 🚫 = not in formula booklet
Rounding Numbers
Rounding rules
There are standardized rules for how to approximate numerical values:
If the digit after the one being rounded off is LESS than 5 (0,1,2,3, or 4), we round down.
If the digit after the one being rounded off is 5 OR MORE (5,6,7,8, or 9), we round up.
1.34∣5→1.351.34∣4→1.34(image)
Significant figures
A significant figure is any digit that is not a leading or trailing zero. To round off to a number of significant figures, count off the specified number of significant figures, then round based off of rounding rules (down if the next digit is less than 5, up if the digit is 5 or more).
NOTE: Unless a question states otherwise, on IB exams, you are expected to give answers to 3 significant figures.
Scientific Notation
Writing numbers in standard form
Scientific notation is a useful way to write large or small numbers in a compact form. It uses powers of 10 to "condense" a lot of digits. Numbers written in scientific notation are of the form
where 1≤a<10 and k∈Z.
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Scientific notation is sometimes called "standard form."
Multiplying & dividing numbers in scientific notation
We can multiply and divide numbers in scientific form as follows:
Multiplying and dividing numbers in scientific notation relies heavily on exponent rules.