Understand the value of digits in whole numbers up to millions
Read and write numbers with up to 6 digits
Understand place value in decimal numbers (tenths, hundredths, thousandths)
Real-World Applications
Money: Knowing that the 4 in £4,523.67 is worth £4,000 helps you estimate totals quickly.
Data: Reading large figures (population 3,456,782) requires understanding each column's value.
Measurement: 3.074 kg — the 7 is in the hundredths column, worth 0.07 kg.
Place Value in Whole Numbers
Every digit in a number has a POSITION that determines its VALUE. The position is called its place value. Reading from right to left: Units, Tens, Hundreds, Thousands, Ten-thousands, Hundred-thousands, Millions.
Example 1 — What is the value of the digit 6 in 3,456,782?
Step 1
Write the number in a place value chart (see diagram above)
Step 2
6 is in the THOUSANDS column
Step 3
The value is \(6 \times 1{,}000 = 6{,}000\)
Step 4
Answer: The digit 6 represents six thousand (6,000)
Example 2 — Write 400,000 + 30,000 + 200 + 8 as a number
Step 1
Identify each column: 4 in hundred-thousands, 3 in ten-thousands, 0 in thousands, 2 in hundreds, 0 in tens, 8 in units
Step 2
Write left to right, filling zeros: 430,208
Step 3
Answer: 430,208
Example 2b — Write "four hundred and six thousand, and fifty-two" in figures
Step 1
Break the words into place-value chunks: "four hundred thousand" = 400,000; "six thousand" = 6,000; "and fifty-two" = 52.
Step 2
Add the chunks together, just like expanded form: \(400{,}000 + 6{,}000 + 52\).
Step 3
Write left to right, filling any empty columns with zero: 406,052.
Step 4
Answer: 406,052
You can also go the other way: 406,052 in words is "four hundred and six thousand, and fifty-two" — read each group of digits (hundred-thousands to thousands, then hundreds to units) and name its value.
Tip: The digit 0 is a placeholder. In 5,047 the hundreds digit is 0 — without it, 547 would be a different number entirely.
✓ Quick Check 1 — Place value in whole numbers
Question 1 of 10
Place Value in Decimal Numbers
The decimal point separates the whole number from the fractional part. After the decimal point, reading left to right: tenths (÷10), hundredths (÷100), thousandths (÷1000).
Example 3 — What is the value of the digit 7 in 3.074?
Step 1
Place the digits in a decimal place value chart (see diagram above)
Step 2
7 is in the HUNDREDTHS column (second column after the decimal point)
Step 3
Value \(= 7 \times \frac{1}{100} = \frac{7}{100} = 0.07\)
Step 4
Answer: The digit 7 represents seven hundredths (0.07)
Example 4 — Write 4 + 0.2 + 0.05 + 0.009 as a decimal number
Answer each question, then click Check All to see how you did.
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Question
Answer
Result
1
What is the value of 5 in 35,240?
2
What digit is in the hundredths column of 7.348?
3
Write 200,000 + 4,000 + 60 + 3 as a number.
4
What is the value of 9 in 6.093?
5
Which is larger: 0.4 or 0.39?
6
Order: 2.3, 2.03, 2.33 smallest first (write with commas)
7
What is the value of 7 in 1,705,200?
8
In 0.604, what column is the 4 in?
9
What is the value of 2 in 82,406?
10
Write 50,000 + 3,000 + 90 + 7 as a number.
⚠ Things to Watch Out For
Zero as a placeholder: In 3,047 the zero holds the hundreds place. Without it, 347 has a completely different value — never drop zeros in the middle of a number.
Confusing the column names: Thousands, hundreds, tens, units — work right to left. The digit immediately left of the decimal point is always units.
Mixing up tenths and tens: Tenths (0.1) are to the RIGHT of the decimal point. Tens (10) are to the LEFT. They are very different in value.
Writing large numbers: Use commas to group digits in threes from the right: 1,234,567 — not 12,34,567.
Decimal point position: The decimal point always sits between the units digit and the tenths digit — never move it without changing the value.