Knowledge Organiser: Place Value and Ordering
Key Terms
- Place value: The value of a digit based on its position in a number
- Decimal point: Separates whole numbers (left) from decimal parts (right)
- Placeholder zero: A zero that holds a column but has no value itself
- Tenths: First decimal place: one tenth of one unit
- Significant figure: A digit that carries meaning in the precision of a number
- Inequality: A statement showing one value is greater or less than another
Must-Know Facts
- Each column is 10× bigger than the column to its right
- 0.8 = 0.80 but 0.8 and 0.08 are very different values
- Negative numbers closer to zero are bigger (−2 > −5)
- To order decimals: line up decimal points, add zeros, compare left to right
- Leading zeros (0.0067) are NOT significant figures
- Arrow in < or > always points to the smaller number
- ≤ means less than or equal to; ≥ means greater than or equal to
Key Methods
- Value of a digit: identify its column, multiply digit × column value
- Ordering decimals: pad with zeros so all have same length, then compare digit by digit
- Writing large numbers: split into thousands group + remainder
- Counting significant figures: start from first non-zero digit
Common Mistakes
- 0.8 vs 0.08: Students confuse these: always compare digit by digit after aligning decimal points
- Ordering negatives: Writing −5 > −2 is wrong; on a number line, −2 is further right so −2 > −5
- Significant figures of leading zeros: In 0.0067, the zeros are NOT significant: count from the first non-zero digit
- Inequality direction: Forgetting which way < and > point: the arrow always points to the smaller number
- Place value columns: Confusing hundredths with hundreds: read column name carefully