Numbers, Place Value & the Number Line
Most math anxiety is not about talent — it is about gaps. A shaky grip on place value or signed numbers makes algebra feel like magic instead of logic. This course rebuilds the foundation so every later step has a clear reason.
Why rebuild from zero?
Most math anxiety is not about talent — it is about gaps. A shaky grip on place value or signed numbers makes algebra feel like magic instead of logic. This course rebuilds the foundation so every later step has a clear reason.
We start with what a number actually means: how many, how far, and in which direction — then connect that meaning to symbols you already recognise.
Place value in base 10
In 4, prov the digits mean 4 thousands, 0 hundreds, 5 tens, and 2 ones. Moving a digit one place left multiplies its value by 10; one place right divides by 10.
- Ones → tens → hundreds → thousands (×10 each step left).
- Decimals go the other way: tenths, hundredths, thousandths (÷10 each step right).
- Zero is a placeholder: without it, 405 and 45 would look the same.
The number line
Every real number sits on a line. Zero is the origin. Positive numbers go right; negative numbers go left. Distance from zero is the absolute value |x|.
- Comparing: the number farther right is larger (so −2 > −5).
- Absolute value: |−7| = 7 and |7| = 7 — size without direction.
- Integers: …, −2, −1, 0, 1, 2, … — whole steps on the line.