โ† All topics๐Ÿงฉ Number Types & Place ValueMaths
Number Theory ยท Topic 1 of 9

๐Ÿงฉ Number Types & Place Value

Numbers come in families, and each family sits inside a bigger one. Knowing the family lets you answer many one-line questions instantly.

The idea in one minute

Natural โ†’ Whole โ†’ Integer โ†’ Rational โ†’ Real. Each set adds something to the one before it: whole adds 0, integers add negatives, rationals add fractions, reals add irrationals like โˆš2 and ฯ€.

Two quick tests examiners love:

โ€ข Irrational โˆšn โ€” โˆšn is a clean whole number only when n is a perfect square. So โˆš9 = 3 (rational), but โˆš7 is irrational.

โ€ข Place value vs face value โ€” face value is just the digit; place value depends on the column. In 582 the 8 has face value 8 but place value 80.

๐ŸงฉNumber ClassifierType a number โ€” see what it is
Enter a whole number
โœ“ Natural1, 2, 3 โ€ฆ
โœ“ Wholeincludes 0
โœ“ Integerno fraction part
โœ“ Evendivisible by 2
ยท Oddnot divisible by 2
ยท Primeexactly 2 factors
โœ“ Compositemore than 2 factors
ยท Perfect squaren = k ร— k
ยท Perfect cuben = k ร— k ร— k

In 582, the place value of 8 is . Is โˆš2 rational or irrational? .

๐Ÿ“Practice Questions

Q1Which of these is an irrational number?

Q2In the number 4382, what is the place value of 3?

Q3Which statement is always true?