Scientific Notation Calculator
Convert numbers to and from scientific, E and engineering notation, raise to any power or root, simplify square roots, do long division step by step and round numbers exactly by decimal places, significant figures or any multiple.
Scientific notation calculator
Exponent calculator and square root calculator
Long division calculator
Rounding calculator (round off calculator)
How scientific notation works
Scientific notation writes a number as a × 10ⁿ, with 1 ≤ a < 10. Move the decimal point until one non-zero digit is left of it; the number of places moved is the exponent (positive for big numbers, negative for small ones): 123,456 = 1.23456 × 10⁵; 0.000789 = 7.89 × 10⁻⁴. Calculators and spreadsheets show the same thing as E notation (1.23456E5). Engineering notation uses exponents that are multiples of 3 (123.456 × 10³), matching kilo, mega, milli and micro.
Exponent calculator and square root calculator
bⁿ multiplies b by itself n times: 2¹⁰ = 1,024. Whole-number powers are shown exactly, even when they're huge (2¹⁰⁰ has 31 digits). A negative exponent means a reciprocal (2⁻³ = 1/8) and a fractional exponent is a root (271/3 = 3). To simplify a square root, pull out the largest square factor: √72 = √(36 × 2) = 6√2 ≈ 8.4853.
Long division calculator
Divide digit by digit: bring down, divide, multiply, subtract. 7,145 ÷ 6: 7 ÷ 6 = 1 r 1; 11 ÷ 6 = 1 r 5; 54 ÷ 6 = 9 r 0; 5 ÷ 6 = 0 r 5. So 7,145 ÷ 6 = 1,190 R 5, or 1,190.8333…. The table shows each step for your numbers.
Rounding calculator: half up vs half to even
Round half up (the school method) rounds 5s away from zero: 2.675 to two decimal places is 2.68. Many calculators and spreadsheets wrongly give 2.67 because 2.675 can't be stored exactly in binary; this round off calculator works with the exact decimal. Banker's rounding (half to even) rounds ties to the even digit, so 2.665 becomes 2.66 and 2.675 becomes 2.68; it avoids bias when adding many rounded numbers. Significant figures count from the first non-zero digit: 0.004567 to 3 significant figures is 0.00457.
Common questions
How do I write 123,456 in scientific notation?
1.23456 × 10⁵.
How do I write 0.000789 in scientific notation?
7.89 × 10⁻⁴.
What is the simplified square root of 72?
6√2 ≈ 8.4853.
What is 7,145 divided by 6?
1,190 remainder 5 (1,190.8333…).
What is 2.675 rounded to 2 decimal places?
2.68 with round-half-up; some software shows 2.67 because of binary floating point.
Sources
Related
General information, not financial, tax or legal advice. Check important numbers with the official source before acting on them.