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Lena Hoffmann

Articles by Lena Hoffmann

Science & education writer · View profile

· 2 min read

Roman Numerals Explained

Seven letters, added or subtracted. Here's what each stands for, how the subtractive pairs work, how to write any number, and where they still appear.

· 3 min read

How to Find a Cube Root by Hand

A step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.

· 3 min read

What Is a Factorial? n! Explained Simply

A factorial multiplies every whole number down to 1. Learn what n! means, how fast it grows, and why it powers permutations and combinations.

· 3 min read

What Grade Do You Need on Your Final?

Work out the exact final-exam grade you need to hit your target, from your current grade and the exam's weight. Here's the formula and an example.

· 2 min read

The Pythagorean Theorem Explained

In a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.

· 3 min read

LCM and GCD Explained

The GCD is the biggest shared divisor; the LCM is the smallest shared multiple. Here's what each means, how to find them with prime factors, and the shortcut linking them.

· 2 min read

Probability Basics, With Examples

Probability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.

· 3 min read

How to Calculate Volume

Volume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.

· 3 min read

Circle: Circumference and Area

Circumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.

· 2 min read

How to Convert a Fraction to a Decimal

Divide the top number by the bottom. Here's the rule, why some fractions repeat, how to round them, and how to turn the result into a percentage.

· 3 min read

How to Simplify a Ratio

Divide both sides by their greatest common divisor. Here's what a ratio is, how to reduce it, why units must match first, and how to compare ratios.

· 3 min read

Scientific Notation Explained

Scientific notation writes huge and tiny numbers as a value times a power of ten. Here's how to write it, read the exponent, and convert back.

· 3 min read

How to Count Business Days

Business days are weekdays minus holidays. Here's what counts, how to work them out between two dates, why holidays complicate it, and where it matters.

· 3 min read

How to Calculate a Weighted Average

A weighted average gives some values more influence than others. Learn the Σ(w·x) / Σw formula with grade and portfolio examples you can follow step by step.

· 3 min read

What Week Number Is It?

Week numbers run from 1 to 52 or 53. Here's how the ISO 8601 system numbers them, why some years have 53 weeks, and where businesses use them.

· 3 min read

How to Add or Subtract Days from a Date

Count forward to add, backward to subtract, rolling over month ends. Here's how, why month lengths and leap years trip you up, and when weekends count.