Math Tools
5 free tools — precise calculations, instant results.
scientific notation
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fraction decimal
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ratio simplifier
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percentage change
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prime factorization
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About Math Tools
Math tools help you solve common mathematical problems including scientific notation, fraction-decimal conversion, ratio simplification, percentage change, and prime factorization. All calculations use verified mathematical algorithms.
Scientific Notation: Working with Very Large and Small Numbers
Scientific notation expresses numbers as a × 10^b, where 1 ≤ |a| < 10. This makes very large numbers (the distance to the nearest star: 4.07 × 10^13 km) and very small numbers (the mass of an electron: 9.11 × 10^-31 kg) readable and comparable. In programming, this is written as 4.07e13 or 9.11e-31.
Fractions, Decimals, and Percentages
These three representations of rational numbers are interchangeable. To convert a fraction to decimal, divide numerator by denominator (3/4 = 0.75). To convert decimal to percent, multiply by 100 (0.75 = 75%). To convert percent to fraction, write as N/100 and simplify (75% = 75/100 = 3/4). Understanding this triangle is fundamental for financial calculations, probability, and statistics.
Prime Factorization and Its Applications
Every integer greater than 1 is either prime (divisible only by 1 and itself) or can be expressed as a unique product of primes (Fundamental Theorem of Arithmetic). For example, 360 = 2³ × 3² × 5. Prime factorization is used to find GCD and LCM, simplify fractions, and is the mathematical foundation of RSA cryptography—which secures virtually all internet communications.
Frequently Asked Questions
What is the difference between percentage and percentage change?
Percentage expresses a ratio as parts per hundred: 25% of 80 = 20. Percentage change measures how much a value has increased or decreased: ((New − Old) ÷ Old) × 100. A price that rises from $50 to $60 has a 20% percentage change.
How do I simplify a ratio?
Divide both sides of the ratio by their Greatest Common Divisor (GCD). For example, 24:36 has a GCD of 12, so 24÷12 : 36÷12 = 2:3.
What is a prime number?
A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. The first primes are 2, 3, 5, 7, 11, 13, 17, 19, 23. 2 is the only even prime number.