Place Value and Ordering
Place value is the value a digit has because of its position within a number, so the 4 in 4,000 is worth four thousand rather than just four. 11+ papers test place value alongside ordering, comparing and rounding whole numbers and decimals, always without a calculator.
Before you start
No specific prerequisites - this is a good place to start.
Method
- Identify the place-value columns in the number: units, tens, hundreds, thousands, and tenths, hundredths after the decimal point.
- To order numbers, compare digits from the left-hand, most significant column first, only moving to the next column when digits are tied.
- Line decimals up by their decimal point, padding with zeros, before comparing, since 0.4 and 0.40 are equal but 0.4 and 0.04 are not.
- To round, look at the digit immediately to the right of the rounding place: 5 or more rounds up, below 5 rounds down or stays the same.
- For negative numbers, remember the number line runs from very negative on the left to very positive on the right, so -8 is smaller than -3.
- Check your final order or rounded value makes sense against the size of the original numbers.
Worked example
Order these numbers from smallest to largest: 5.06, 5.6, 5.605, 5.65
- Write every number to three decimal places by padding with zeros: 5.060, 5.600, 5.605, 5.650.
- Compare the units digit first: all four numbers have 5 units, so compare the tenths digit next.
- 5.060 has 0 tenths, which is smaller than the 6 tenths in the other three numbers, so 5.06 is the smallest.
- Among 5.600, 5.605 and 5.650, compare the hundredths digit: 5.650 has 5 hundredths, larger than the 0 hundredths in the other two, so 5.65 is the largest of these three.
- Compare 5.600 and 5.605 using the thousandths digit: 5.605 has 5 thousandths against 0, so 5.605 is larger than 5.6.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
The distance from a town to the coast is recorded as 84,306 metres. (a) What is the value of the digit 4 in 84,306? (b) Round 84,306 to the nearest thousand.
Order these values from smallest to largest, showing your method: 7/10, 0.68, 65%, 0.7
A 4-digit whole number has these properties: the units digit is 3; the thousands digit is triple the units digit; the hundreds digit is 2 less than the thousands digit; the tens digit is 0. Find the number, showing your working.
Free printable worksheet
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