Place value
The same digit can be worth 3, 30 or 0.3. What decides which, and what does that let a written number do?
Where you are 15 inside
What this area is about
Our numerals bundle in tens: ten ones make a ten, ten tens a hundred, and the column a digit sits in decides what it is worth. Each place is worth ten times the place to its right, and the same rule, carried past the decimal point, gives tenths and hundredths.
How these fit together
Building the places. Teen numbers as ten and some more, tens and ones and trading ten for one make the bundles.
Reading and writing. Numbers to 1,000, numbers to one million, the place value chart, expanded form and decimal place value.
Using the places. Comparing and ordering, rounding, multiplying and dividing by ten, one hundred and one thousand, and the same moves for decimals: multiplying and dividing.
Other systems. Other bases bundle in a size other than ten; tally marks and Roman numerals have no columns: each mark or letter has a fixed value, added or sometimes subtracted.
A path through it
Teen numbers, tens and ones, then trading and numbers to 1{,}000. The chart and comparing follow, then expanded form and numbers to one million. Decimal place value needs expanded form and comparing; rounding needs decimals and numbers to a million. Shifting by ten comes after the chart and decimals, and before the decimal versions. Other bases follow expanded form; Roman numerals fit anywhere.
Next come multi-digit addition, partial products and scientific notation.