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Number System - Place value up to millions

Grade 5IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Place Value Chart: Understanding positions from Ones up to Millions (Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions).

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Value vs. Place Value: 'Place Value' is the position of a digit (e.g., Millions), while 'Value' is the worth of that digit (e.g., 5,000,000).

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Standard Form: The usual way to write a number using digits (e.g., 2,340,000).

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Expanded Form: Writing a number as the sum of the values of its digits (e.g., 2,000,000 + 300,000 + 40,000).

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Word Form: Writing the number using words (e.g., Two million, three hundred forty thousand).

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Comparing and Ordering: Using symbols like <, >, and = to compare numbers based on their highest place value positions.

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Rounding: Approximating numbers to the nearest 10, 100, 1,000, 10,000, or 100,000.

📐Formulae

Value=Digit×Place Value Position\text{Value} = \text{Digit} \times \text{Place Value Position}

Expanded Form=(d6×1,000,000)+(d5×100,000)+(d4×10,000)+…\text{Expanded Form} = (d_6 \times 1,000,000) + (d_5 \times 100,000) + (d_4 \times 10,000) + \dots

Rounding Rule:If the digit to the right is ≥5, round up; if <5, stay the same.\text{Rounding Rule}: \text{If the digit to the right is } \ge 5, \text{ round up; if } < 5, \text{ stay the same.}

💡Examples

Problem 1:

Identify the value and the place value of the digit 7 in the number 4,723,051.

Solution:

Place Value: Hundred Thousands; Value: 700,000

Explanation:

The digit 7 is in the sixth position from the right, which corresponds to the Hundred Thousands place. Therefore, its value is 7×100,000=700,0007 \times 100,000 = 700,000.

Problem 2:

Write the number 'Five million, sixty-two thousand, eight hundred four' in standard form and expanded form.

Solution:

Standard: 5,062,804; Expanded: 5,000,000 + 60,000 + 2,000 + 800 + 4

Explanation:

The word 'million' indicates 5 in the millions place. 'Sixty-two thousand' means 6 in the ten thousands and 2 in the thousands. Since there are no 'hundred thousands' or 'tens', we use 0 as a placeholder.

Problem 3:

Round 3,456,210 to the nearest hundred thousand.

Solution:

3,500,000

Explanation:

To round to the nearest hundred thousand, look at the ten thousands digit (5). Since it is 5 or greater, round the hundred thousands digit (4) up to 5, and change all digits to the right to zero.

Problem 4:

Compare the numbers using <, >, or =: 1,205,600 ___ 1,250,600

Solution:

1,205,600 < 1,250,600

Explanation:

Comparing from left to right: both have 1 in the millions and 2 in the hundred thousands. In the ten thousands place, 0 is less than 5, so the first number is smaller.