Order of Operations Checklist
1
Step 1: Solve everything inside parentheses/brackets first
2
Step 2: Evaluate exponents and roots (powers, square roots)
3
Step 3: Perform multiplication and division, left to right
4
Step 4: Perform addition and subtraction, left to right
| Function | Symbol / Key | Example Input | Result |
|---|---|---|---|
| Sine (degrees) | sin | sin(30°) | 0.5 |
| Common logarithm (base 10) | log | log(100) | 2 |
| Natural logarithm (base e) | ln | ln(e) | 1 |
| Square root | √ | √81 | 9 |
| Exponent | ^ or xʸ | 2^5 | 32 |
| Factorial | ! | 5! | 120 |
| Combinations | nCr | 5 nCr 2 | 10 |
Example 1 Walkthrough
1
Step 1: No parentheses to resolve
2
Step 2: Evaluate the exponent first: 2² = 4
3
Step 3: Multiply: 4 × 4 = 16
4
Step 4: Add: 3 + 16 = 19
5
Result: 19
Example 2 Walkthrough
1
Step 1: Confirm the calculator is in degree mode
2
Step 2: sin(30°) = 0.5
3
Step 3: cos(60°) = 0.5
4
Step 4: Add the results: 0.5 + 0.5 = 1
5
Result: 1
Example 3 Walkthrough
1
Step 1: log(1000) means log base 10 of 1000, which equals 3 (since 10³ = 1000)
2
Step 2: Evaluate the exponent: 2³ = 8
3
Step 3: Add the results: 3 + 8 = 11
4
Result: 11
Example 4 Walkthrough
1
Step 1: Sum the data set: 4 + 8 + 6 + 10 = 28
2
Step 2: Divide by the number of values: 28 / 4
3
Mean result: 7
4
Step 3: For 6 nCr 2, use the formula n! / (r!(n-r)!)
5
Step 4: 6! = 720, 2! = 2, 4! = 24, so 720 / (2 × 24)
6
Combinations result: 15
- Wrong angle mode: mixing up degrees and radians is the single most common trigonometry mistake. Always check the mode indicator (often labeled DEG or RAD) before evaluating any trig function.
- Missing parentheses around a whole numerator or denominator: typing 5+3/2 gives 5 + 1.5 = 6.5, while (5+3)/2 correctly gives 4. If a fraction has more than one term on top or bottom, wrap it in parentheses.
- Confusing log and ln: "log" on most calculators means base-10 logarithm, while "ln" means natural logarithm (base e). Using the wrong one will silently give an incorrect answer.
- Forgetting to close parentheses: an unclosed parenthesis can make the calculator apply an operation to more (or less) of the expression than intended.
- Rounding too early: rounding an intermediate result before the final step can compound small errors, especially in multi-step trigonometry or logarithm problems.
Q1What is the difference between a scientific calculator and a basic calculator?
A basic calculator only performs the four basic operations (addition, subtraction, multiplication, division), while a scientific calculator adds trigonometric, logarithmic, exponential, and root functions, along with support for order of operations and parentheses.
Q2How do I know if my calculator is in degree or radian mode?
Most scientific calculators show a small DEG or RAD indicator on the display, or you can test it by evaluating sin(90); in degree mode this equals 1, while in radian mode it will be a different decimal value.
Q3What does the log button calculate?
On most scientific calculators, the log button calculates the base-10 logarithm. For natural logarithm (base e), use the separate ln button.
Q4Can a scientific calculator handle order of operations automatically?
Yes. Modern scientific calculators automatically apply standard order of operations (PEMDAS/BODMAS) to any expression you type in, as long as you enter parentheses correctly around grouped terms.
Q5Does a scientific calculator do statistics?
Many scientific calculators include a statistics mode for mean, standard deviation, and regression, along with combinatorics functions like factorial, permutations (nPr), and combinations (nCr).
Q6What does nCr mean on a scientific calculator?
nCr calculates combinations — the number of ways to choose r items from a set of n items where order doesn't matter, using the formula n! / (r!(n-r)!).