Number and Numeration
What the exam tests
Number and numeration checks whether you can read, write, order and round whole numbers, and use place value, factors, multiples and Roman numerals accurately.
Core rules
- In a place-value chart, each position is ten times the value of the position on its right. The 7 in 47,306 has place value 7,000, while its face value is 7.
- Expanded form breaks a number into the value of each digit: 47,306 = 40,000 + 7,000 + 300 + 6.
- To compare numbers, compare digits from the left; the first different digit decides.
- To round to a place, look at the digit immediately to the right. If it is 5 or more, round up; if less than 5, keep the digit.
- A factor divides a number exactly. A prime number has exactly two factors: 1 and itself. Multiples come from multiplying by 1, 2, 3, ...
Worked example
Write 47,306 in expanded form and round it to the nearest thousand. Expanded form: 40,000 + 7,000 + 300 + 6. For rounding, the thousands digit is 7. The digit to its right is 3 (hundreds). Since 3 < 5, the thousands digit stays 7 and the rest become zeros: 47,000.
Traps that cost marks
Do not confuse face value with place value. Keep zero as a placeholder when writing numerals. When rounding 4,999 to the nearest thousand, the answer is 5,000, not 4,000, because the hundreds digit is 9. In Roman numerals, a smaller symbol before a larger one is subtracted: IV = 4, IX = 9, XL = 40.