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1.3 Expanded notation




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)

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