Maths · Topic 1 of 44 · Free lesson
Place value
Place value is what a digit is worth because of where it sits. Each column is worth ten times the column on its right, and the decimal point separates the whole numbers from the tenths and hundredths.
What it is
Place value is what a digit is worth because of where it sits. Each column is worth ten times the column on its right, and the decimal point separates the whole numbers from the tenths and hundredths.
Levels 1–3 · Number
Remember
Th H T O . t h th: each column is worth 10 times the one on its right.
Light bulb
To × or ÷ by 10, 100 or 1,000, the digits move, not the point. The decimal point stays still and every digit slides the same number of places.
Getting started (Levels 1–2)
The method
- 1Write the number in a place value chart, lining up the decimal point.
- 2Read the heading above the digit: that is what it is worth.
- 3× 10, 100 or 1,000: move every digit 1, 2 or 3 places left. Dividing moves them right.
- 4Fill any empty columns before the point with placeholder zeros.
Worked example
What is the 6 worth in 4,682?
- 1.The 6 is in the hundreds (H) column
- =So it is worth 600
Understanding it
Our number system uses only ten digits, 0 to 9. When a column fills up with ten, those ten swap for one in the next column to the left. That is why each column is worth ten times the one on its right, and why the same digit 3 can mean 3, 30 or 300.
Picture the columns as a row of boxes on a shelf, with the decimal point fixed like a nail. Multiplying by 10 slides every digit one box to the left, so each digit is worth ten times more. Dividing slides them right. Zeros are simply empty boxes that keep the other digits in place.
Place value sits under almost every other topic: rounding, column sums, decimals and changing units like 2.4 km into 2,400 m. The 11+ tests it with 'what is the digit worth', 'write in figures', ordering decimals and × or ÷ by 10, 100 and 1,000, often inside a money or measures question.
Key words
- Digit
- One of the ten symbols, 0 to 9, used to write numbers.
- Place value
- What a digit is worth because of the column it is in.
- Decimal point
- The dot between the whole numbers and the parts of a whole.
- Placeholder zero
- A zero that keeps the other digits in their right columns.
- Tenth
- One whole split into ten equal parts: 0.1.
Step by step
Work out 650 ÷ 1,000
- 1.÷ 1,000 moves every digit three places right
- 2.6 hundreds become 6 tenths; 5 tens become 5 hundredths
- 3.No ones are left, so a zero holds the ones column
- =650 ÷ 1,000 = 0.65
Common mistakes
Working out 3.07 × 10 as 3.070, by just adding a zero on the end.
Move every digit one place left instead: 3.07 × 10 = 30.7.
Saying the 4 in 4,682 is worth 4.
Read its column heading: it is in the thousands, so it is worth 4,000.
Writing two thousand and fifty as 20,050 or 2,50.
Use one digit per column and fill the gaps: 2 thousands, 0 hundreds, 5 tens, 0 ones = 2,050.
Exam level (Levels 3–4)
Work out 42.5 ÷ 100
- 1.÷ 100 moves every digit two places right
- 2.The 4 tens become 4 tenths; a zero holds the ones
- =42.5 ÷ 100 = 0.425
Watch out
0.45 is not bigger than 0.5. Compare column by column from the left: 0.5 = 0.50, and 5 tenths beats 4 tenths.
Exam tip
For 'write in figures' questions, write one digit per column and fill the gaps with zeros: five million, forty thousand and six is 5,040,006.
Quick check
Work each one out, then tap to see the answer.
1 · Level 1
What is the 9 worth in 59,214?
Show the answer
9,000
2 · Level 2
Which is the largest: 0.7, 0.65, 0.07 or 0.699?
Show the answer
0.7
3 · Level 3
Work out 3.07 × 1,000
Show the answer
3,070
11+ example questions, worked
Real 11+ style questions, solved for you. Read how each one is done.
11+ example question 1
Work out: 33.61 × 10
- A33.61
- B336.1
- C3.361
- D3,361
- E43.61
How to solve it: Multiplying by 10 moves the digits 1 place to the left. 33.61 × 10 = 336.1.
11+ example question 2
Write 98 in Roman numerals.
- AXCVIII
- BLXXXXVIII
- CXCIX
- DXCVII
- ECXVIII
How to solve it: Split 98 into place values and write each part: 98 = 90 + 5 + 3, which is XC + V + III = XCVIII.
Try it
Have a go on your own. We'll mark each one as you go.
5 questions
1.What is 100 less than 40,645?
2.What is 10 more than 60,785?
3.What is the value of the digit 7 in 7,991?
4.What is the value of the digit 1 in 1,904?
5.Write this number in figures: five hundred and ninety-four thousand and sixty-five