P2B · Fractions & decimals · DEC.OPERATIONS

Operate with decimals

Intuition

Understand first, compress later.

Fractions, decimals and percentages are different representations of the same quantity idea.

Switch representations

Place value chart425.6

digitplace value

Each column is worth ten times its right-hand neighbour — the digit says how many, the column says of what. Written out place by place, the values add back to 425.6.

Formal view

You can operate with decimals when you can recognise the underlying objects, select valid rules and check each step for equivalence or logical implication.

Why does it work?

This skill sits on a prerequisite network. If a step is unstable, repair the missing prerequisite instead of merely doing more items of the same type.