Disclaimer
Math Lantern’s calculators show worked solutions so you can learn a method and check your own work. They are not an answer service for exams, and they are not statistical, financial or legal advice. Try each problem first, then compare your working line by line.
Where a teacher’s rules come first
Do not open the steps where your teacher, exam board or employer forbids outside help. If calculators are not allowed in class, that rule applies here too.
Numbers have limits
Browsers store numbers in binary, so some decimals cannot be held exactly: in JavaScript, 0.1 + 0.2 gives 0.30000000000000004. Math Lantern rounds results to six decimals, which hides that noise, but very large or very small values can still round. Check results that matter by a second method.
Why the last decimal can differ
Your paper working may round earlier than the calculator does. One third is 0.33 at two decimals, 0.3333 at four and 0.333333 at six, yet exactly 1/3 on paper. Round only at the end and the answers agree.
Assumptions behind a tool
Some tools assume conditions: independent events in the probability calculator, a fixed chance p on every trial in the binomial calculator, or numbers separated by commas in the statistics solver. If your situation differs, the result may not apply.
No professional advice
Nothing here is advice for medicine, finance, engineering or law. Ask a qualified professional about decisions that carry risk. Names of tests and publishers belong to their owners and appear only for identification.
Frequently asked questions
Can I cite Math Lantern in homework?
Cite your textbook for the method. You may say you checked your working with a calculator if your teacher allows it.
Why does my answer differ in the last decimal?
Rounding. The calculator shows six decimals while paper working may round earlier.
Is Math Lantern linked to an exam board or publisher?
No. Names appear only to identify tests or books.
Back to the Math Lantern step-by-step calculators. The terms of use and privacy policy cover the rest.