Question: A museum exhibit displays a number system from an ancient civilization, where a base-$b$ number $213_b$ equals $47$ in base ten. What is the value of $b$?

Thu, 30 Apr 2026 20:57:33 +0000

**Discover the Hidden Math Behind an Ancient Numerical Mystery**
Curious About How Ancient Civilizations Shaped Modern Numbers?
One of the most fascinating exhibits in U.S. museums highlights how numerical systems from long-ago cultures differ from today’s base-10 standard—especially a striking example: the number $213_b$, which, when interpreted in base $b$, equals $47$ in base ten. This blend of history, logic, and cultural curiosity is resonating across digital platforms, especially in mobile search results where users seek clear, reliable answers on number systems. ### Why a Museum Exhibit on Ancient Number Bases Is Catching National Attention The revival of interest in ancient math systems is more than academic—it speaks to broader trends in cultural heritage, STEM education, and digital storytelling. Museums increasingly showcase how early civilizations, such as the Sumerians, Mayans, or others, developed base-$b$ systems to solve practical problems, from trade to astronomy. $213_b = 47_{10}$, for instance, demonstrates how place value and positional notation allowed complex calculations without modern arithmetic. This exhibit connects visitors to global intellectual history, sparking dialogue about innovation across time and borders—trends that amplify its appeal in digital spaces where users explore cultural insights while seeking clear, contextual knowledge. ### How to Transform $213_b$ into Base Ten: A Clear Breakdown