Merge pull request #3089 from chilipenko/fix-range-for-number-type

Several fixes for number type

Author: iliakan

1-js/02-first-steps/05-types/article.md

@@ -68,9 +68,9 @@ We'll see more about working with numbers in the chapter <info:number>.
 
 ## BigInt [#bigint-type]
 
-In JavaScript, the "number" type cannot represent integer values larger than <code>(2<sup>53</sup>-1)</code> (that's `9007199254740991`), or less than <code>-(2<sup>53</sup>-1)</code> for negatives. It's a technical limitation caused by their internal representation.
+In JavaScript, the "number" type cannot safely represent integer values larger than <code>(2<sup>53</sup>-1)</code> (that's `9007199254740991`), or less than <code>-(2<sup>53</sup>-1)</code> for negatives. Technically "number" type can store larger integers (up to <code>1.7976931348623157 * 10<sup>308</sup></code>), but outside of the safe integer range <code>±(2<sup>53</sup>-1)</code> a lot of integer values can't be represented using this data type: some of them are "missed" due to the limitation caused by their internal binary representation. For example, all the odd integers greater than <code>(2<sup>53</sup>-1)</code> are "missed" in the "number" type.
 
-For most purposes that's quite enough, but sometimes we need really big numbers, e.g. for cryptography or microsecond-precision timestamps.
+For most purposes <code>±(2<sup>53</sup>-1)</code> range is quite enough, but sometimes we need the entire range of really big integers without missing any of them, e.g. for cryptography or microsecond-precision timestamps.
 
 `BigInt` type was recently added to the language to represent integers of arbitrary length.
 

1-js/05-data-types/02-number/article.md

@@ -2,9 +2,9 @@
 
 In modern JavaScript, there are two types of numbers:
 
-1. Regular numbers in JavaScript are stored in 64-bit format [IEEE-754](https://en.wikipedia.org/wiki/IEEE_754-2008_revision), also known as "double precision floating point numbers". These are numbers that we're using most of the time, and we'll talk about them in this chapter.
+1. Regular numbers in JavaScript are stored in 64-bit format [IEEE-754](https://en.wikipedia.org/wiki/IEEE_754), also known as "double precision floating point numbers". These are numbers that we're using most of the time, and we'll talk about them in this chapter.
 
-2. BigInt numbers represent integers of arbitrary length. They are sometimes needed because a regular number can't safely exceed <code>2<sup>53</sup></code> or be less than <code>-2<sup>53</sup></code>. As bigints are used in few special areas, we devote them a special chapter <info:bigint>.
+2. BigInt numbers represent integers of arbitrary length. They are sometimes needed because a regular integer number can't safely exceed <code>(2<sup>53</sup>-1)</code> or be less than <code>-(2<sup>53</sup>-1)</code>, as we mentioned earlier in the chapter <info:types>. As bigints are used in few special areas, we devote them a special chapter <info:bigint>.
 
 So here we'll talk about regular numbers. Let's expand our knowledge of them.
 
@@ -192,7 +192,7 @@ There are two ways to do so:
 
 ## Imprecise calculations
 
-Internally, a number is represented in 64-bit format [IEEE-754](https://en.wikipedia.org/wiki/IEEE_754-2008_revision), so there are exactly 64 bits to store a number: 52 of them are used to store the digits, 11 of them store the position of the decimal point (they are zero for integer numbers), and 1 bit is for the sign.
+Internally, a number is represented in 64-bit format [IEEE-754](https://en.wikipedia.org/wiki/IEEE_754), so there are exactly 64 bits to store a number: 52 of them are used to store the digits, 11 of them store the position of the decimal point, and 1 bit is for the sign.
 
 If a number is really huge, it may overflow the 64-bit storage and become a special numeric value `Infinity`: