How to Use This Scientific Notation Calculator
- Convert a number: type any number and get it in scientific notation, E notation, standard form, and engineering notation. Choose a number of significant figures to round it at the same time.
- Calculate: enter two numbers as a coefficient and a power of ten, pick an operation, and get the answer with every step shown and the result rounded by the significant figure rules.
The calculator works with exact decimals, so it never introduces rounding errors of its own, and it keeps the significant figures you type: 3.00 × 108 stays at three.
How to Convert a Number to Scientific Notation
- Move the decimal point until exactly one nonzero digit is in front of it.
- Count how many places you moved it. That count is the exponent.
- Moving the point left (a large number) makes the exponent positive; moving it right (a small number) makes it negative.
| Number | Scientific notation | Why |
|---|---|---|
| 0.000452 | 4.52 × 10−4 | The point moves 4 places right. |
| 6,022,000 | 6.022 × 106 | The point moves 6 places left; the trailing zeros are placeholders. |
| 0.0250 | 2.50 × 10−2 | The final zero is significant, so it stays in the coefficient. |
Keep every significant digit in the coefficient and drop placeholder zeros. If you are unsure which zeros count, the sig fig calculator highlights them digit by digit.
How to Convert Scientific Notation to Standard Form
Move the decimal point the number of places given by the exponent: to the right for a positive exponent, to the left for a negative one, filling empty places with zeros. 3.00 × 108 becomes 300,000,000, and 6.56 × 10−7 becomes 0.000000656. Large numbers written in standard form can hide their precision, because 300,000,000 looks like it has one significant figure, so chemistry answers usually stay in scientific notation.
How to Multiply and Divide in Scientific Notation
Multiply or divide the coefficients, then add the exponents when multiplying or subtract them when dividing. If the new coefficient is 10 or more, or less than 1, move the decimal point and adjust the exponent.
| Chemistry calculation | Steps | Answer |
|---|---|---|
| Particles in 0.250 mol: (6.022 × 1023)(0.250) | 6.022 × 0.250 = 1.5055; exponent stays 23 | 1.51 × 1023 |
| Frequency of 656 nm light: (3.00 × 108) ÷ (6.56 × 10−7) | 3.00 ÷ 6.56 = 0.4573; 8 − (−7) = 15; rewrite as 4.573 × 1014 | 4.57 × 1014 s−1 |
Both answers keep three significant figures because the least precise number in each has three. Mole-to-particle steps like the first are covered in AP Chemistry Avogadro’s number, and wavelength-to-frequency problems like the second in AP Chemistry photon energy.
How to Add and Subtract in Scientific Notation
Rewrite the numbers so they share the same power of ten, then add or subtract the coefficients. For 3.2 × 104 + 4.5 × 103, rewrite the second number as 0.45 × 104, add to get 3.65 × 104, then round to the thousands place set by 3.2 × 104: 3.7 × 104. Addition follows the decimal-place rule, not the significant-figure rule, and the reasons are worked through in AP Chemistry scientific notation.
E Notation, Engineering Notation, and Calculator Entry
- E notation is how calculators and spreadsheets display scientific notation: 6.022E23 means 6.022 × 1023.
- Engineering notation keeps the exponent a multiple of 3, so 4.52 × 10−4 becomes 452 × 10−6, matching metric prefixes such as micro.
- On a TI-84, enter scientific notation with the EE key: 6.022 EE 23. Typing 6.022 × 10 EE 23 gives an answer ten times too large, because EE already means “times ten to the power of.”
College Board’s AP calculator policy allows a calculator on both sections of the AP Chemistry exam, including the built-in Desmos calculator in Bluebook, so practice entering powers of ten on the calculator you will actually use. To see how your practice-test results translate into an AP score, try the AP Chem Score Calculator.
Related Resources
- AP Chem Score Calculator
- AP Chemistry Scientific Notation
- Sig Fig Calculator
- AP Chemistry Avogadro’s Number
- AP Chemistry Photon Energy
- AP Chemistry pH Scale
- AP Chemistry Study Guide
Frequently Asked Questions
How do you write 0.00052 in scientific notation?
Move the decimal point four places to the right to get a coefficient between 1 and 10: 5.2. Moving right makes the exponent negative, so 0.00052 = 5.2 × 10^-4.
What does E mean on a calculator?
E stands for "times ten to the power of." A display of 6.022E23 means 6.022 × 10^23. On a TI-84 you type it with the EE key, so enter 6.022 EE 23, not 6.022 × 10 EE 23, which is ten times too large.
How many significant figures does a number in scientific notation have?
Count only the digits in the coefficient. 3.00 × 10^8 has 3 significant figures and 6.022 × 10^23 has 4. The power of ten never adds or removes significant figures.
Can you use a calculator on the AP Chemistry exam?
Yes. College Board's current AP calculator policy allows a calculator on both the multiple-choice and free-response sections of AP Chemistry, and the Bluebook app includes a built-in Desmos calculator. A scientific or graphing calculator is recommended. Websites like this one cannot be used during the exam.
What is the difference between scientific notation and engineering notation?
Scientific notation always has one nonzero digit before the decimal point, such as 4.52 × 10^-4. Engineering notation keeps the exponent a multiple of 3, so the same number is 452 × 10^-6, which lines up with metric prefixes such as micro.
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