Place Value & Ordering
Understanding the value of each digit, comparing and ordering numbers, rounding and working with negative numbers.
What is Place Value & Ordering?
Place value means understanding what each digit in a number is worth depending on its position. For example, in the number 4,725, the digit 4 is worth 4,000, the 7 is worth 700, the 2 is worth 20 and the 5 is worth 5.
In the 11+ exam, place value questions test whether your child can identify digit values, compare and order numbers (including decimals), round numbers to the nearest 10, 100 or 1,000, and work with negative numbers on a number line.
This is one of the most fundamental maths skills – it underpins almost every other topic, so it is well worth getting right.
Step-by-Step Method
Know your place value columns
From right to left: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions. For decimals: tenths, hundredths, thousandths after the decimal point.
Read the question carefully
Check whether it asks for the value of a digit (e.g. “what is the value of the 3?”) or the digit in a particular column (e.g. “what digit is in the hundreds place?”).
For ordering, compare from left to right
Start with the highest place value column and compare digits. If they are the same, move one column to the right. The first difference tells you the order.
For rounding, look at the digit to the right
If the digit to the right of the rounding column is 5 or more, round up. If it is 4 or less, round down (keep the digit the same).
For negative numbers, use a number line
Picture a number line in your head. Numbers to the right are larger. So -3 is greater than -7 because -3 is further to the right.
Worked Examples
In the number 56,382, what is the value of the digit 3?
Working
- Write out the place value columns: 5 = ten thousands, 6 = thousands, 3 = hundreds, 8 = tens, 2 = ones
- The digit 3 is in the hundreds column
- So its value is 3 x 100 = 300
Put these numbers in order from smallest to largest: 0.45, 0.405, 0.5, 0.045
Working
- Make all numbers the same length by adding trailing zeros: 0.450, 0.405, 0.500, 0.045
- Now compare: 045, 405, 500, 045
- Smallest first: 0.045 (45 thousandths), then 0.405, then 0.45, then 0.5
Round 4,673 to the nearest hundred.
Working
- The hundreds digit is 6 (in 4,673)
- Look at the digit to the right: 7
- 7 is 5 or more, so round up: 6 becomes 7
- Replace everything after the hundreds column with zeros
Common Mistakes
Thinking 0.45 is smaller than 0.405 because 45 is smaller than 405.
Add trailing zeros so both have the same number of decimal places: 0.450 vs 0.405. Now 450 > 405, so 0.45 is larger.
Confusing the digit with its value – saying the 3 in 4,362 is worth “3”.
The digit is 3, but its value depends on its position. In the hundreds column, its value is 300.
Thinking -3 is less than -7 because 3 is smaller than 7.
With negative numbers, the one closer to zero is larger. -3 is greater than -7. Draw a number line if unsure.
Top Tips
- When ordering decimals, always add trailing zeros so all numbers have the same number of decimal places. This makes comparison much easier.
- Remember: the value of a digit = the digit x its column value. So 5 in the thousands column = 5,000.
- For rounding, circle the digit you are rounding to and underline the digit to its right. That underlined digit tells you whether to round up or down.
- With negative numbers, think of temperature. -2 degrees is warmer (bigger) than -10 degrees.
- If a question says “ascending order” it means smallest to largest. “Descending order” means largest to smallest.
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