A scientific calculator is a type of electronic calculator, usually handheld, designed to calculate problems in science, engineering, and mathematics. They have more functions than a standard four-function calculator and are widely used by students and professionals.

Key features typically include:

• Arithmetic operations (addition, subtraction, multiplication, division)
• Trigonometric functions (sin, cos, tan, and their inverses)
• Logarithmic and exponential functions (log, ln, eˣ, 10ˣ)
• Powers and roots (x², x³, xʸ, √, ³√)
• Parentheses for order of operations
• Scientific notation display and input
• Memory functions

Some advanced scientific calculators may also handle statistics, complex numbers, binary/octal/hexadecimal conversions, and basic programming.

Using a scientific calculator involves several common steps:

1. Power On: Most have an ON or AC (All Clear) button.
2. Mode Selection (if applicable):
   • Angle Mode: Ensure you're in Degrees (DEG), Radians (RAD), or Gradians (GRAD) as needed for trigonometric functions. This is often changed via a MODE or DRG key.
   • Display Mode: Some calculators allow switching between normal, scientific (SCI), or engineering (ENG) notation for results.
3. Entering Numbers: Use the number keys 0-9 and the decimal point . key.
4. Basic Operations: Use +, -, ×, ÷.
5. Order of Operations: Scientific calculators follow mathematical order of operations (PEMDAS/BODMAS). Use parentheses ( ) to group operations and override the default order.
6. Functions:
   • Most functions (e.g., sin, log, √) are pressed before entering the number. For example, to find the square root of 9, you'd press √ then 9 then =.
   • Some functions, like squaring (x²), might be pressed after the number.
7. Equals: Press the = key to calculate and display the result.
8. Clear:
   • C or CE (Clear Entry) usually clears the last number entered.
   • AC (All Clear) clears the entire calculation and resets the calculator.
9. Second/Shift Functions: Many keys have a secondary function printed above them. Access these using a SHIFT, 2nd, or INV key. For example, SHIFT then sin might give you sin⁻¹ (arcsin).

Always refer to your specific calculator's manual for detailed instructions, as button labels and operations can vary slightly between models.

Scientific notation is a way to express very large or very small numbers. It's typically written as a × 10^b.

Entering Numbers in Scientific Notation:

1. Enter the significand (the 'a' part). For example, for 3.5 × 10⁶, type 3.5.
2. Press the scientific notation key. This is often labeled EXP, EE, ×10ⁿ, or ×10ˣ.
   • This key replaces typing "× 10 ^". Do not type the multiplication symbol or "10".
3. Enter the exponent (the 'b' part). For 3.5 × 10⁶, type 6.
4. If the exponent is negative (e.g., 2.1 × 10^-4), enter the significand (2.1), press the EXP (or similar) key, then use the change sign key (+/- or (-)) and then enter the exponent (4). Some calculators allow entering the minus sign before the exponent digit.

Example: To enter 6.022 × 10²³:

6.022 EXP 23

Reading Scientific Notation on the Display:

Calculators display scientific notation in various ways, often using an "E" or a space before the exponent:

• 3.5E6 or 3.5 06 means 3.5 × 10⁶
• 2.1E-4 or 2.1 -04 means 2.1 × 10^-4

Calculator Mode for Scientific Notation:

Many calculators can be set to always display results in scientific notation (SCI mode) or engineering notation (ENG mode, where the exponent is a multiple of 3). This is usually done via a MODE or SETUP key. In normal (NORM or FLO) mode, the calculator will only switch to scientific notation if the number is too large or too small to fit on the display.

Many scientific calculators have a dedicated fraction key. It's often labeled a b/c, x/y, ■/■, or similar.

Entering Fractions:

• Proper Fractions (e.g., 3/4): Type 3 a b/c 4. The display might show something like "3 L 4" or "3/4".
• Improper Fractions (e.g., 7/5): Type 7 a b/c 5.
• Mixed Numbers (e.g., 1 and 2/3): Type 1 a b/c 2 a b/c 3. The display might show "1 L 2 L 3".

Operations with Fractions:

Once entered, you can perform arithmetic operations (+, -, ×, ÷) with fractions just like with whole numbers. The calculator will typically display the result as a fraction (often simplified) or a mixed number.

Converting Between Fractions and Decimals:

Most calculators with a fraction key can convert between fractional and decimal representations. This might be done by pressing the fraction key again, or a SHIFT + fraction key, or a dedicated F↔D key (Fraction to Decimal).

If your calculator doesn't have a dedicated fraction key:

You can still work with fractions by treating them as division problems. For example, to calculate 3/4 + 1/2:

Enter: ( 3 ÷ 4 ) + ( 1 ÷ 2 ) =

The result will be a decimal (e.g., 1.25). You would then need to convert this back to a fraction manually if needed.

Scientific calculators offer several ways to calculate exponents (raising a number to a power):

• Squaring (x²): Most calculators have a dedicated x² key. To calculate 5², you would type 5 x² =.
• Cubing (x³): Some calculators have an x³ key. If not, use the general power key.
• General Powers (xʸ or ^): For any power, use the general exponent key. This is often labeled xʸ, yˣ, ^, or EXP (be careful not to confuse this with the scientific notation EXP key if they are separate).

  To calculate 2⁵ (2 to the power of 5):

  Type 2 xʸ (or ^) 5 =.

• Powers of 10 (10ˣ): Often there's a dedicated 10ˣ key, usually as a shift function of the log key. To calculate 10³, you might press SHIFT log (to get 10ˣ) then 3 =.
• Negative Exponents: To calculate 4^-2, you would type 4 xʸ (or ^) (-) 2 = or 4 xʸ (or ^) 2 +/- =, depending on how your calculator handles negative number input.
• Fractional Exponents (Roots): An exponent of 1/2 is a square root, 1/3 is a cube root, etc. For example, 9^1/2 is √9. You can enter this as 9 xʸ ( 1 ÷ 2 ) =. Many calculators also have dedicated root keys (√, ³√, ˣ√).

The constant 'e' (Euler's number, approximately 2.71828) is fundamental in mathematics. Calculating e raised to a power (eˣ) is a common operation.

Most scientific calculators have a dedicated eˣ key. This key is often the secondary function of the ln (natural logarithm) key.

To calculate eˣ:

1. Press the SHIFT or 2nd key.
2. Press the ln key (which should activate its eˣ function). The display might show "e^(" or similar.
3. Enter the value of x (the exponent).
4. If your calculator added an opening parenthesis, you might need to close it with ).
5. Press =.

Example: Calculate e²

SHIFT ln (to get eˣ) 2 =

The result should be approximately 7.389.

Some calculators might have a direct eˣ key, or you might first enter the exponent 'x' and then press the eˣ key. Consult your calculator's manual if unsure.

The ln key on a scientific calculator stands for natural logarithm.

A logarithm answers the question: "To what power must a specific base number be raised to get another number?"

• The common logarithm uses base 10 and is usually denoted by the log key. So, log(100) = 2 because 10² = 100.
• The natural logarithm uses the mathematical constant 'e' (Euler's number, approximately 2.71828) as its base. So, ln(x) is the power to which 'e' must be raised to get x. For example, ln(e²) = 2.

How to use the ln key:

1. Press the ln key.
2. Enter the number for which you want to find the natural logarithm.
3. Press =.

Example: Calculate ln(10)

ln 10 =

The result will be approximately 2.30258.

The natural logarithm and its inverse function, eˣ (the natural exponential function, often SHIFT + ln), are crucial in calculus, physics, engineering, economics, and many other scientific fields.

TI-84 and TI-84 Plus: These are primarily graphing calculators. While they perform all the functions of a scientific calculator (trigonometry, logarithms, exponents, etc.), their main distinguishing feature is their ability to plot graphs of functions, perform statistical analysis with graphical output, and often run programs. So, yes, a TI-84 includes scientific calculator functionality, but it's much more than just a scientific calculator.

TI-30XS MultiView™ and TI-30X IIS: These models are classic examples of scientific calculators. They are designed for advanced math and science calculations but typically do not have graphing capabilities. They are very common in middle school, high school, and some college-level courses.

In summary:

• TI-30XS, TI-30X IIS: Yes, these are scientific calculators.
• TI-84, TI-84 Plus: These are graphing calculators that contain and extend the functionality of a scientific calculator.

While both are advanced calculators, they have key differences:

Scientific Calculator:

• Primary Function: Performing numerical calculations for science, engineering, and math (trigonometry, logarithms, exponents, scientific notation, etc.).
• Display: Typically one or a few lines, showing input and output numerically. Some advanced models (like TI-30XS MultiView™) can show expressions as they'd appear in a textbook.
• Graphing: Generally no graphing capabilities.
• Programming: Limited or no programming features.
• Cost: Usually less expensive than graphing calculators.
• Common Use: Middle school, high school, some introductory college courses, professional work not requiring graphing.

Graphing Calculator:

• Primary Function: In addition to all scientific calculator functions, its main feature is to plot graphs of equations and functions.
• Display: Larger, high-resolution screen (often pixel-based) to display graphs, tables, and more complex mathematical expressions.
• Graphing: Extensive capabilities to plot functions, analyze graphs (find intersections, maxima/minima, etc.), and sometimes plot statistical data or 3D graphs.
• Programming: Often support programming in languages like TI-BASIC, allowing users to create custom programs and applications.
• Advanced Features: May include Computer Algebra Systems (CAS) for symbolic manipulation, spreadsheet capabilities, data collection interfaces for science experiments, and more.
• Cost: Generally more expensive.
• Common Use: Advanced high school math (Pre-calculus, Calculus), college-level math and science courses, engineering, statistics.

In essence, a graphing calculator is a superset of a scientific calculator, adding graphical and often programming capabilities.

Turning Off:

• Many scientific calculators have an OFF key, often as a secondary function (accessed by pressing SHIFT or 2nd first, then another key, e.g., AC).
• Some calculators turn off automatically after a period of inactivity to save battery.
• If there's no explicit OFF key, the auto-power-off feature is usually the primary way it conserves power.

Resetting:

Resetting a calculator typically returns it to its factory default settings (e.g., angle mode to Degrees, normal display mode, clears memory).

• Soft Reset (Mode Reset): Some calculators have a "reset" option within their MODE or SETUP menu. This might reset calculation modes, angle units, and display formats without clearing memory registers.
• Hard Reset (Full Reset):
  • Many calculators have a small, recessed reset button on the back. You'll need a pointed object like a paperclip to press it.
  • Some models might have a key combination for resetting (e.g., holding ON while pressing another key, or a specific sequence from the MODE menu).
  • Removing the batteries for a few minutes and then reinserting them can sometimes perform a reset, though this is not always guaranteed or recommended as the primary method.

Important: Always consult your calculator's specific user manual for the correct procedures for turning off and resetting, as methods can vary significantly between brands and models. A hard reset will typically erase any stored data or programs.

Many scientific calculators, especially those with a dedicated fraction key (a b/c, ■/■, etc.), can convert decimals to fractions.

General Steps:

1. Enter the decimal number you want to convert (e.g., 0.75).
2. Press the key or key combination that converts decimals to fractions. This varies by calculator:
   • Sometimes, pressing the fraction key (a b/c) itself after a decimal input will convert it.
   • There might be a dedicated "Fraction to Decimal" conversion key, often labeled F↔D or similar (sometimes as a SHIFT function).
   • On some calculators, after entering the decimal and pressing =, you might then press a key sequence to display it as a fraction.

Example: Convert 0.75 to a fraction

Type: 0.75 = (to store it or ensure it's the current value) then press your calculator's F↔D key or the fraction key. The display should change to show "3/4" or "3 L 4".

Limitations:

• Calculators can usually only convert terminating decimals or decimals that represent simple repeating patterns into fractions.
• There might be a limit to the complexity of the fraction (denominator size) that the calculator can handle or display.
• Irrational numbers (like π or √2) cannot be expressed as simple fractions.

If your calculator does not have this feature, you'll need to convert decimals to fractions manually using mathematical methods.

Your iPhone has a built-in scientific calculator:

1. Open the standard Calculator app.
2. By default, it opens in standard mode (portrait orientation).
3. Turn your iPhone to landscape orientation (sideways).

When in landscape mode, the calculator app will automatically switch to scientific mode, revealing many more functions like trigonometric (sin, cos, tan), logarithmic (log₁₀, ln), exponential (eˣ, 10ˣ), powers (x², x³, xʸ), roots (√, ³√, ʸ√x), parentheses, and more.

You can also find many third-party scientific calculator apps on the App Store, some of which offer even more advanced features, different layouts, or graphing capabilities (e.g., PCalc, Calcbot, Desmos).

Cost:

The price of a scientific calculator can vary widely based on its features, brand, and capabilities:

• Basic Scientific Calculators: These can range from $10 to $25. They are suitable for most middle school, high school, and some basic college math and science needs (e.g., Texas Instruments TI-30X IIS, Casio fx-300ES PLUS).
• Advanced Scientific Calculators: Calculators with more features like "textbook display" (showing expressions as written), solar power, or more statistical functions might cost $20 to $50 (e.g., Texas Instruments TI-36X Pro, Casio fx-115ES PLUS).
• Graphing Calculators (which include scientific functions): These are significantly more expensive, typically ranging from $90 to $150+ (e.g., Texas Instruments TI-84 Plus CE, Casio fx-CG50).

Where to Buy:

You can purchase scientific calculators from various places:

• Office Supply Stores: Staples, Office Depot/OfficeMax.
• Electronics Stores: Best Buy.
• General Retailers: Walmart, Target.
• Online Retailers: Amazon, eBay, and the websites of office supply or electronics stores.
• Bookstores: College and university bookstores often stock calculators required for courses.
• Drugstores/Pharmacies: Some larger chains might carry basic models.

When buying, consider the requirements for your school or work, and check if specific models are recommended or prohibited for exams.

Calculator policies for exams vary greatly depending on the educational institution, the specific course, the level of study, and the standardized test.

• Some exams allow any scientific calculator but may prohibit graphing calculators or those with CAS (Computer Algebra Systems).
• Some exams specify a list of approved calculator models. You must use one from this list.
• Some exams prohibit all calculators.
• Standardized tests like the SAT, ACT, AP exams, IB exams, etc., have very specific calculator policies that you must adhere to. These policies often detail which types and models are permitted, restricted, or banned.

It is crucial to always check the specific calculator policy for any exam you are taking. This information is usually provided by the instructor, the school, or the testing organization.

Using a prohibited calculator can lead to disqualification or other serious consequences.

Whether you need a scientific calculator for algebra depends on the level and curriculum.

• Introductory Algebra (e.g., Algebra 1): A scientific calculator can be helpful for checking arithmetic, working with exponents, square roots, and evaluating expressions with specific values. However, a strong emphasis is usually placed on learning to perform these operations manually and understanding the algebraic concepts. Some instructors may even restrict calculator use initially to build foundational skills.
• Intermediate/Advanced Algebra (e.g., Algebra 2, Pre-calculus): A scientific calculator becomes more essential. Topics like logarithms, exponential functions, complex numbers, and more advanced functions often require a scientific calculator for efficient computation. Graphing calculators are often recommended or required at this level for visualizing functions and solving equations graphically.

Benefits of using a scientific calculator in algebra:

• Quickly performs complex arithmetic.
• Handles scientific notation, logarithms, exponents, and trigonometric functions (which may appear in applied algebra problems).
• Helps in checking answers derived manually.
• Allows focus on algebraic concepts rather than getting bogged down in tedious calculations.

Always follow your instructor's guidelines regarding calculator use. They will specify if a calculator is allowed, recommended, or required, and which type is appropriate for the course.