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Year 7 Mathematics · Number and Algebra · 8m read

Whole Numbers, Place Value and Rounding

Ever wonder why 5,000 and 50 are completely different even though they both have a 5? That's place value at work — it's how the position of each digit tells you what it's actually worth. Learning to read, write, and round whole numbers gives you the solid foundation every mathematician needs, making everything from everyday shopping to complex calculations feel manageable and logical.

Learning objective: Read, write and round whole numbers using place value.

By the end of this lesson you can:

  • I read and write numbers up to millions.
  • I identify the value of each digit.
  • I round to the nearest 10, 100, 1 000 and 1 000 000.

Place value chart

Each digit carries a VALUE determined by its POSITION in the number.

PLACE VALUE TABLE (right → left):
┌──────────┬──────────┬──────────┬──────────┬──────────┬──────────┬──────────┐
│ Millions │ HThou │ TThou │Thousands │ Hundreds │ Tens │ Ones │
│ 1000000 │ 100000 │ 10000 │ 1000 │ 100 │ 10 │ 1 │
└──────────┴──────────┴──────────┴──────────┴──────────┴──────────┴──────────┘

EXAMPLE: 3 248 517
3 × 1 000 000 = 3 000 000
2 × 100 000 = 200 000
4 × 10 000 = 40 000
8 × 1 000 = 8 000
5 × 100 = 500
1 × 10 = 10
7 × 1 = 7

ROUNDING RULE:
1. Find the digit at the rounding place.
2. Look ONE digit to its RIGHT (the "decider").
3. Decider ≥ 5 → round UP (add 1 to rounding digit, replace rest with zeros).
4. Decider < 5 → round DOWN (keep rounding digit, replace rest with zeros).

Example: Round 47 382 to the nearest 1 000.
• Thousands digit = 7. Decider = 3 (hundreds). 3 < 5 → round DOWN → 47 000.

House address analogy. Think of each place as a floor in a building. The ones floor is the ground floor, tens is 1st floor, hundreds is 2nd floor, etc. The digit tells you HOW MANY rooms on each floor.

Place value rules cheatsheet

  • Digit vs value: In 4 820, the digit 4 sits in the thousands place, so its VALUE is 4 000 — not just 4.
  • Zero placeholders: In 307, the 0 means "no tens". It MUST be written to hold the place correctly.
  • Rounding tie-breaker: Decider = 5 always rounds UP. "5 and above, give it a shove."

Place value and rounding

  • Place value: \text{value} = \text{digit} \times \text{place}
  • Round to nearest 10: \text{look at units digit; }\geq 5 \Rightarrow \text{up}

Quick reference

| Place | Value of 7 in 4 783 512 |
|---|---|
| Millions | 4 000 000 |
| Hundred thousands | 700 000 |
| Ten thousands | 80 000 |
| Rounding rule | Look at the next digit: 5 or more → round up |
| 4 783 512 to nearest thousand | 4 784 000 |

Worked example (Easy)

Round 6 482 to the nearest 100.

  1. Identify rounding place. Nearest 100 → hundreds digit. In 6 482, hundreds digit = 4.
  2. Find the decider. One place to the right of hundreds → tens digit = 8.
  3. Apply rule. 8 ≥ 5 → round UP. 6 482 → 6 500.

Answer: 6 500

Worked example (Medium)

A stadium holds 83 746 people. Round to the nearest 10 000.

  1. Find ten-thousands digit. In 83 746, the ten-thousands digit is 8.
  2. Decider. One place right → thousands digit = 3.
  3. Apply rule. 3 < 5 → round DOWN → 80 000.

Answer: 80 000

Common mistakes

  • Rounding to the wrong place value Students confuse which digit to look at when rounding — they count from the wrong end or mix up the decider. Fix: Underline the rounding digit FIRST, then circle the digit immediately to its RIGHT (the decider). Only then apply the rule.
  • Forgetting to replace digits after the rounding place with zeros Students round the digit correctly but leave the remaining digits unchanged: 47 382 rounded to nearest 1 000 becomes "47 000", not "47 382" with just the 7 changed. Fix: After rounding, ALL digits to the RIGHT of the rounding place become 0. This is what "rounding" means — simplifying.
  • Confusing digit with value Students say the 5 in 3 508 has a value of 5, not 500. Fix: Always state the PLACE: "The digit 5 is in the hundreds place, so its value is 500." Value = digit × place value.

Why place value is the foundation of all mathematics

Our number system — the Hindu-Arabic system — is one of humanity's greatest inventions. Before it, Romans used letters (XIV = 14), and calculations were extremely difficult. The breakthrough was positional notation: the idea that a digit's value depends on its position in the number.

This system uses base 10 (decimal), meaning each position is worth 10 times the one to its right. The digit 3 in 300 is worth ten times more than the 3 in 30, and a hundred times more than the 3 in 3. This simple rule scales infinitely — from ones to billions and beyond.

Rounding is important because real-world measurements are never perfectly precise. When a news report says "approximately 2 million people attended," that's rounding. When a scientist reports a measurement as 4.7 cm, that's rounded to the nearest millimetre. Understanding significant figures and estimation — both built on place value — is essential in science, engineering and everyday life. The skills you learn here underpin every calculation you will ever do.

Practice questions

  1. What is the value of the digit 6 in 2 648 301?

    1. 6
    2. 6 000
    3. 600 000
    4. 60 000

    (1 marks)

  2. Round 7 249 to the nearest 1 000.

    1. 7 000
    2. 7 200
    3. 7 300
    4. 8 000

    (1 marks)

  3. Write the number 4 million, 30 thousand and 8 in digits.

    (2 marks)

Summary

  • Read and write numbers up to millions.
  • Identify the value of each digit.
  • Round to the nearest 10, 100, 1 000 and 1 000 000.

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