How can doubles represent higher numbers than decimals if they can't hold as many significant figures?

I may very well have not the proper understanding of significant figures, but the book

C# 6.0 in a Nutshell by Joseph Albahari and Ben Albahari (O’Reilly).

Copyright 2016 Joseph Albahari and Ben Albahari, 978-1-491-92706-9.

provides the table below for comparing double and decimal:

Is it not counter-intuitive that, on the one hand, a double can hold a smaller quantity of significant figures, while on the other it can represent numbers way bigger than decimal, which can hold a higher quantity of significant figures ?

Solution

Imagine you were told you can store a value, but were given a limitation: You can only store 10 digits, 0-9 and a negative symbol. You can create the rules to decode the value, so you can store any value.

The first way you store things is simply as the value xxxxxxxxxx, meaning the number 123 is stored as 0000000123. Simple to store and read. This is how an int works.

Now you decide you want to store fractional numbers, so you change the rules a bit. Now you store xxxxxxyyyy, where x is the integer portion and y is the fractional portion. So, 123.98 would be stored as 0001239800. This is roughly how a Decimal value works. You can see the largest value I can store is 9999999999, which translates to 999999.9999. This means I have a hard upper limit on the size of the value, but the number of the significant digits is large at 10.

There is a way to store larger values, and that's to store the x and y components for the formula $x*10^y$ in xxxxxxyyyy. So, to store 123.98, you need to store 01239800-2, which I can calculate as $12398*10^{-2}$ . This means I can store much bigger numbers by changing 'y', but the number of significant digits is basically fixed at 6. This is basically how a double works.