How to Use a Scientific Calculator Without Getting the Wrong Answer

Type −3² into one calculator and get 9; type it into another and get −9. Enter sin 30 and get 0.5 on one, −0.988 on another. Both calculators are working correctly; they are making different assumptions about what you meant. A scientific calculator is only as accurate as your understanding of its conventions, and students lose exam marks on exactly these points every year. This guide covers the settings and habits that produce the right answer, using the Scientific Calculator as the reference.

Degrees or radians: the setting that ruins exams

Trigonometric functions need to know the angle unit. In degree mode, sin 30 = 0.5. In radian mode, sin 30 means sin(30 radians) = −0.988. Physics and engineering problems given in degrees need degree mode; calculus, most programming and anything involving π needs radians. Check the mode indicator before every trig calculation. The calculator shows DEG or RAD next to the display; the toggle is one tap.

Conversion if you need it: radians = degrees × π ÷ 180. So 30° = π⁄6 ≈ 0.5236 rad.

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Order of operations and the −3² problem

Standard precedence: parentheses, then exponents, then multiplication and division (left to right), then addition and subtraction. Under those rules, −3² is −(3²) = −9, because the exponent binds tighter than the negation. Most scientific calculators follow this, and a mathematician will tell you it is correct. Some basic calculators and spreadsheets (Excel included) treat the minus as part of the number and return 9. If you mean (−3)², type the parentheses. Never rely on the calculator to guess.

Other precedence traps:

• 1/2x: is it (1⁄2)x or 1⁄(2x)? Calculators differ. Use parentheses.
• 2^3^2: right-associative in maths (2^(3^2) = 512), but some calculators compute left to right (8^2 = 64). Parentheses again.
• Implicit multiplication (2(3+4)) is treated as higher precedence than explicit division on some models, which is the source of the viral “8÷2(2+2)” arguments. The answer depends on the convention; write it unambiguously.

The functions and what they’re for

Key	Does	Typical use
x², x³, xʸ	Powers	Area, volume, compound growth
√, ∛, ˣ√y	Roots	Pythagoras, standard deviation
sin cos tan	Trig from angle	Geometry, physics vectors
sin⁻¹ cos⁻¹ tan⁻¹	Angle from ratio (arcsin etc.)	Finding angles in triangles
log	Base-10 logarithm	pH, decibels, orders of magnitude
ln	Natural log (base e)	Growth and decay, calculus
eˣ, 10ˣ	Inverse of ln and log	Undoing a log
n!	Factorial	Permutations, probability
nCr, nPr	Combinations, permutations	“How many ways to choose 3 from 10”
EXP or ×10ˣ	Scientific notation entry	Avogadro’s number, very small measurements
MOD	Remainder	Cyclic calculations, programming
M+ M− MR MC	Memory	Storing an intermediate result
Ans	Previous result	Chaining without retyping

Scientific notation

Large and small numbers appear as 6.022E23 (6.022 × 10²³). To enter one, type the mantissa, press EXP (or ×10ˣ), then the exponent: 6.022 EXP 23. A common error is typing 6.022 × 10 EXP 23, which gives 6.022 × 10²⁴. The EXP key already means “times ten to the”.

Rounding and significant figures

Keep full precision through a calculation and round once at the end. Rounding intermediate steps to three figures, then multiplying, compounds the error. Use the memory or Ans key to carry the unrounded value. When reporting, match the precision of the least precise input: a measurement of 12.3 cm times 4.56 cm is 56.1 cm², not 56.088.

Habits that prevent wrong answers

1. Check DEG/RAD before any trig.
2. Bracket every negative base and every fraction in a denominator.
3. Estimate first. If you expect roughly 50 and get 5,000, a decimal point or an exponent slipped.
4. Re-enter long calculations a second time in a different order (or from the end) and compare.
5. For percentages and unit conversions, the Percentage Calculator and Unit Converter are faster and less error-prone than doing them on a scientific calculator; for fractions, the Fraction Calculator keeps results exact rather than decimal.

Frequently asked questions

Why does my calculator say sin 30 is −0.988?

It is in radian mode. Switch to degrees for angles given in degrees.

Is −3² equal to 9 or −9?

−9 under standard mathematical precedence, because the exponent applies before the negation. Write (−3)² if you want 9.

What is the difference between log and ln?

log is base 10; ln is base e (2.718…). Use ln for growth, decay and calculus; log for pH, decibels and anything defined in powers of ten.

How do I enter a number in scientific notation?

Mantissa, then the EXP or ×10ˣ key, then the exponent. Do not type “× 10” as well.