Place Value and Whole Numbers
Read, write and compare whole numbers up to millions. Understand how each digit's position determines its value.
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Before you read on — quickly: Which number is larger: 4,560,231 or 4,506,321? How do you know? Try it, then check your reasoning as you go.
Every digit in a number has a value based on its position. This is called place value. The place value system uses periods of three digits (hundreds, thousands, millions) separated by commas.
In the number 4,560,231, each digit's position tells us its worth. The 4 is in the millions place, so it represents 4,000,000. The 5 is in the hundred-thousands place, so it represents 500,000. Understanding place value is the foundation for all number work.
Know
- The value of each digit in numbers up to millions
- How commas separate periods of three digits
- The words for each place value position
Understand
- How place value determines a digit's worth
- Why zero is essential as a placeholder
- Why comparing from the left is always correct
Can Do
- Read and write large whole numbers in words and digits
- Compare two large numbers using place value
- Identify the value of any digit in a number
Wrong: "The more digits a number has, the larger it is." 100 has more digits than 99, but 999 > 100.
Right: Start comparing from the highest place value (leftmost digit). The first different digit decides.
Wrong: Writing "five thousand and sixty-two" as 5,602 instead of 5,062.
Right: Use a place value table or say the number out loud. 5,062 = 5 thousands + 0 hundreds + 6 tens + 2 ones.
To read a large number, split it into periods (groups of three digits from the right), then read each period as a 3-digit number followed by the period name.
The number 4,560,231 splits into three periods: 4 (millions), 560 (thousands), and 231 (units). Read it as: "Four million, five hundred and sixty thousand, two hundred and thirty-one."
To write a number in words, work period by period from left to right. Write each period as a 3-digit number in words, then add the period name.
Write 7,030,052 in words. Split: 7 | 030 | 052. Read each: "Seven" + "million" + "thirty" + "thousand" + "and" + "fifty-two". Result: "Seven million, thirty thousand and fifty-two." Note the and before the last part.
To compare two numbers, line up the digits and compare from the left. The first place where the digits differ tells you which number is larger. The > symbol means "greater than" and < means "less than". The open end always faces the larger number.
Compare 5,678,901 and 5,687,109. Line up: millions match (5=5), hundred-thousands match (6=6), but ten-thousands differ: 7 < 8. So 5,687,109 is larger. The alligator eats the bigger number: 5,678,901 < 5,687,109.
Watch Me Solve It · 3 examples
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1Split into periods12 | 045 | 600Start from the left. Three periods: millions, thousands, units.
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2Read each period12 → "twelve million", 045 → "forty-five thousand", 600 → "six hundred"
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3Combine with commas and "and""Twelve million, forty-five thousand and six hundred"No "and" needed before the thousands period — only before the final units part.
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1Identify the position of the digit28,934,105 — the 8 is in the millions periodSplit: 28 | 934 | 105. The 8 sits in the millions group.
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2Determine the place valueThe 8 is in the millions column
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3Calculate the value8 × 1,000,000 = 8,000,000The digit 8 in the millions place represents eight million.
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1Line up the digits by place value9,876,543
9,865,743Both have 7 digits. Start comparing from the left. -
2Compare digit by digit from the leftMillions: 9 = 9 ✓
Hundred-thousands: 8 = 8 ✓
Ten-thousands: 7 > 6 ← this decides! -
3Write the comparison9,876,543 > 9,865,743The first different digit (7 vs 6) at the ten-thousands place tells us the answer.
Place Value Table
- Millions → Hundred-Thousands → Ten-Thousands → Thousands → Hundreds → Tens → Ones
- Each position is 10× the one to its right
- Commas separate every 3 digits (periods)
Reading Numbers
- Split into periods (groups of 3)
- Read each period as a 3-digit number
- Add the period name after each
- Use "and" before the final units part
Writing in Words
- Write periods as words: million, thousand
- Hyphenate numbers 21–99
- Skip leading zeros (030 = thirty)
- Check by reading aloud
Comparing Numbers
- Line up digits by place value
- Compare from left to right
- First different digit decides
- > opens toward the larger number
How are you completing this lesson?
Brain Trainer · 4 problems
Four drill problems to sharpen your place-value skills. Work each, then reveal the answer.
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1 Write 7,005,020 in words.
Split: 7 | 005 | 020. Read: "Seven million, five thousand and twenty."Seven million, five thousand and twenty -
2 What is the value of 6 in 16,284,573?
The 6 is in the millions place (16 | 284 | 573). Value = 6 × 1,000,000.6,000,000 (six million) -
3 Arrange from smallest to largest: 1,111,111 1,101,111 1,110,111
Compare from left: all start 1,1. At hundred-thousands: 0 < 1. Then 1,101,111 vs 1,110,111: ten-thousands 0 < 1.1,101,111 < 1,110,111 < 1,111,111 -
4 Write "three million and twelve" as a number.
3 million + 0 thousand + 12. Need zeros as placeholders for hundred-thousands, ten-thousands, thousands, hundreds, and tens.3,000,012
Quick Check · 5 questions
Show Your Working · 3 questions
Q6. Write 20,307,080 in words. Explain your process step by step.
Q7. Find the value of the underlined digit: 372,908. Explain how you know.
Q8. Find a number between 4,500,000 and 4,600,000 where the digit 7 is worth 70,000. Give two different examples and explain your reasoning.
Quick Check
1. A — 9,000. The 9 is in the thousands place.
2. A — 4,210,000. At hundred-thousands: 2 > 1 > 0.
3. B — "Five million, eighty thousand and sixty." 080 = eighty.
4. C — 3,004,005. Three million + four thousand + five.
5. A — 5,668,901. Subtract 10,000: the 78 becomes 68.
Show Your Working Model Answers
Q6 (3 marks): Split into periods: 20 | 307 | 080 [1]. Read each: "Twenty million" + "three hundred and seven thousand" + "and eighty" [1]. Answer: "Twenty million, three hundred and seven thousand and eighty" [1].
Q7 (2 marks): The 7 is in the ten-thousands place [1]. Its value is 7 × 10,000 = 70,000 (seventy thousand) [1].
Q8 (4 marks): The digit 7 must be in the ten-thousands place for it to be worth 70,000. The number must be between 4,500,000 and 4,600,000, so it starts with 4,57_. Two examples: 4,570,000 and 4,571,234 [2 for correct examples]. Any number 4,570,000 ≤ n ≤ 4,579,999 works because the 7 is in the ten-thousands place [2 for explanation].
The Digit Puzzle
Using the digits 3, 0, 5, 7, 2, 1, 8 each exactly once, make the largest possible number and the smallest possible number. What is the difference between them?
Reveal solution
Largest: arrange digits from largest to left: 8,753,210. Smallest: smallest non-zero digit first, then the rest: 1,023,578. Difference: 8,753,210 − 1,023,578 = 7,729,632.
Periods
Millions | Thousands | Units
Read by period
Read each 3-digit group, add period name
Write in words
Use periods, skip leading zeros, use "and"
Compare left to right
First different digit decides
Zero matters
Placeholder — keeps other digits in position
Commas
Separate every 3 digits from the right
Interactive: Square Root Estimator
Develop your number sense by estimating square roots. A square has a certain area — can you guess its side length?
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