Place value is the foundation of all number work: each digit in a number has a value determined by its position. At KS3 this extends beyond whole numbers into tenths, hundredths, and thousandths. Understanding place value lets you compare, order, and calculate with any number quickly and accurately.
What is place value?
Every digit in a number occupies a column that tells you its value. The decimal point separates the whole-number part (on the left) from the fractional part (on the right).
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Units | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 000 000 | 100 000 | 10 000 | 1 000 | 100 | 10 | 1 | . | 1/10 | 1/100 | 1/1000 |
Example: In the number 3 407.025:
- 3 is in the thousands column: value = 3 000
- 4 is in the hundreds column: value = 400
- 0 is in the tens column: value = 0
- 7 is in the units column: value = 7
- 0 is in the tenths column: value = 0
- 2 is in the hundredths column: value = 0.02 (= 2/100)
- 5 is in the thousandths column: value = 0.005 (= 5/1000)
The number is read as "three thousand, four hundred and seven point zero two five."
What happens when you multiply or divide by 10, 100, or 1000?
Multiplying or dividing by a power of 10 shifts every digit left or right through the place-value columns. The decimal point stays fixed; the digits move.
| Operation | Effect on digits | Example |
|---|---|---|
| × 10 | Move every digit 1 place to the left | 4.7 × 10 = 47 |
| × 100 | Move every digit 2 places to the left | 4.7 × 100 = 470 |
| × 1000 | Move every digit 3 places to the left | 4.7 × 1000 = 4700 |
| ÷ 10 | Move every digit 1 place to the right | 4.7 ÷ 10 = 0.47 |
| ÷ 100 | Move every digit 2 places to the right | 4.7 ÷ 100 = 0.047 |
| ÷ 1000 | Move every digit 3 places to the right | 4.7 ÷ 1000 = 0.0047 |
A common error is to think "moving the decimal point" — but it is cleaner to think of the digits moving while the decimal point stays put. The result is the same, but thinking of it this way avoids confusion with negative numbers.
How do you compare and order decimals?
To order a list of decimals, align the decimal points and then compare digit by digit from left to right.
Worked example: Place these in order from smallest to largest: 0.4, 0.04, 0.403, 0.43, 0.399
Write them aligned:
0.400
0.040
0.403
0.430
0.399
Compare tenths first: 0.04 has 0 tenths → smallest in tenths column. Then 0.399, 0.400, 0.403, 0.430 all have 3 or 4 in tenths.
Order: 0.04, 0.399, 0.4, 0.403, 0.43
A common mistake: thinking 0.4 < 0.04 because 4 < 40. That confuses place value with digit value. 0.4 = 0.400, which has a 4 in the tenths column; 0.04 has a 0 in tenths and a 4 in hundredths — it is ten times smaller.
How do you write a number from its digit values?
Worked example: Write as a single decimal: 4 thousands + 6 tens + 3 tenths + 8 thousandths.
| Thousands | Hundreds | Tens | Units | . | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|---|
| 4 | 0 | 6 | 0 | . | 3 | 0 | 8 |
Answer: 4 060.308
Note the placeholder zeros in the hundreds, units, and hundredths columns — without them the number would change completely.
How do decimals connect to fractions?
Place value columns to the right of the decimal point represent fractions:
- Tenths: 0.3 = 3/10
- Hundredths: 0.07 = 7/100
- Thousandths: 0.009 = 9/1000
For numbers with multiple decimal digits, combine: 0.125 = 1/10 + 2/100 + 5/1000 = 100/1000 + 20/1000 + 5/1000 = 125/1000 = 1/8
This connection is why understanding place value makes converting fractions to decimals and back much easier.
How do you use place value to estimate calculations?
Worked example: Estimate 4.97 × 302.
- 4.97 ≈ 5 (round to 1 significant figure)
- 302 ≈ 300 (round to 1 significant figure)
- Estimate = 5 × 300 = 1 500
Exact answer: 4.97 × 302 = 1 500.94. The estimate is very close, confirming no major errors.
Estimation using place value is especially useful to catch errors caused by misplacing the decimal point. If your calculator gives 15 009, you know the decimal point is in the wrong place.
Frequently asked questions
Why do we write 0.07 instead of .07?
The leading zero before the decimal point makes clear there is no whole-number part and prevents the decimal point from being missed. In formal mathematics and all UK examinations you should always write the leading zero: 0.07, not .07.
What is the difference between the number of decimal places and significant figures?
Decimal places count the digits after the decimal point: 3.405 has 3 decimal places. Significant figures count meaningful digits starting from the first non-zero digit: 0.0340 has 3 significant figures (3, 4, and the final 0). Place value underpins both concepts — you need to know which column a digit is in to count correctly.
Can place value help with mental multiplication?
Yes. For example, 35 × 40 = 35 × 4 × 10 = 140 × 10 = 1 400. Breaking 40 into 4 × 10 uses place value to simplify the multiplication. Similarly, 0.35 × 40 = 35 × 40 ÷ 100 = 1 400 ÷ 100 = 14. Thinking in terms of place value columns makes these shortcuts clear.
How does place value extend beyond thousandths?
The pattern continues: ten-thousandths (0.0001 = 10⁻⁴), hundred-thousandths (0.00001 = 10⁻⁵), and so on. In science and standard form, these tiny values appear regularly. Each column to the right is one tenth of the previous column, following the same rule as the whole-number side (each column to the left is ten times the previous).
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