AI Tutor
Imagine writing a number like one billion over and over in your math notebook — writing nine zeros every single time gets exhausting fast!
Mathematicians solved this problem by using a clever shorthand based on multiplying tens.

Powers of Ten

An exponent is a small number placed at the top-right of a base number that tells you how many times to multiply that base by itself.
When the base is 10, the exponent tells you exactly how many zeros follow the 1. For example, 10310^3 means 10×10×1010 \times 10 \times 10, which equals 1,0001,000.
How can we use these handy powers of ten to break down an entire multi-digit number?

Writing Expanded Notation

Expanded notation shows the value of each digit by multiplying that digit by its place value written as a power of ten.
Take the number 5,3825,382: we multiply each digit by its place value power and add them together: (5×103)+(3×102)+(8×101)+(2×100)(5 \times 10^3) + (3 \times 10^2) + (8 \times 10^1) + (2 \times 10^0).
What happens when a large number has zeros sitting in the middle?

Dealing with Zeros