# Introduction

We can express a number as the sum of its place values.

For example, the place values present in “12345” are “10,000”, “2,000”, “300”, “40” and “5”. These can be summed to provide $10,000+2,000+300+40+5=12345$

Alternatively, we can break this up into $1(10,000) + 2(1,000) + 3(100) + 4(10) + 5(1) = 12345$

This is called expanded notation.

Sometimes it can be expressed as $1*10,000+2*1,000+3*100+4*10+5*1=12345$, but I’ve used brackets to make it easier to observe.

You can convert expanded notation back into simple form, such that $5(10,000)+3(1,000)+0(100)+5(10)+3(1)=53,053$

Although we’ve so far used (10,000), (1,000), (100), (10), (1), we can replace this with the information:

• $10=10^1$
• $100= 10^2$
• $1,000= 10^3$
• $10,000= 10^4$

For example, instead of writing 12345 as we had above, it would now be $1(10^4)+2(10^3)+3(10^2)+4(10^1)+5 (10^0)$