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Really Big and Really Small Numbers

Master really big and really small numbers with interactive lessons and practice problems! Designed for students like you!

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Really Big and Really Small Numbers

Study Guide

Key Definition

Large numbers like a billion and trillion are represented using powers of ten such as $10^9$ and $10^{12}$.

Important Notes

The American billion is $10^9$.
The British billion was traditionally $10^{12}$.
India uses lakh ($1,00,000$) and crore ($1,00,00,000$).
Scientific notation is useful for expressing very large and small numbers.
Review exponent properties for better understanding.

Mathematical Notation

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

$10^n$ represents ten raised to the power of n

Remember to use proper notation when solving problems

Why It Works

Using powers of ten like $10^9$ allows for easier comparison and calculation with very large numbers.

Remember

In scientific notation, numbers are expressed as $a \times 10^n$ where $1 \leq a < 10$.

Quick Reference

Million:$10^6$

Billion:$10^9$

Trillion:$10^{12}$

Understanding Really Big and Really Small Numbers

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Numbers can grow very large or very small. We use powers of ten to write them compactly. For example, $10^3 = 1,000$ and $10^{-3} = 0.001$. Positive exponents shift the decimal to the right, negative exponents shift it to the left.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which of the following represents one billion in American terms?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a number is expressed in scientific notation as $3.45 \times 10^8$, think about how you would convert it back to a standard number.

Challenge Quiz

Single Choice Quiz

Advanced

In British terms, what was traditionally called a billion?

Recap

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Review key concepts and takeaways