6 — Whole Numbers and Place Value

Whole Numbers and Place Value

Learn More · ID: E7D03151

Place value is like giving each digit in a number its own special address! Every position in a number has a different value - the same digit can be worth 1, 10, 100, or even millions depending on where it sits. Learning place value helps you understand huge numbers like the population of your city or the distance to the moon.

Tip

Each place value is 10 times bigger than the place to its right. For example: thousands are 10 times bigger than hundreds, and hundreds are 10 times bigger than tens.

Whole Numbers and Place Value - Chapter Overview · 1:10

Worked Example

Problem

What is the place value of the digit 7 in the number 47,382?

Solution

The digit 7 is in the thousands place, so its value is 7,000.

Solution

Explanation

  1. 1Write out the number with place value labels: 4 (ten thousands), 7 (thousands), 3 (hundreds), 8 (tens), 2 (ones).
  2. 2Find the digit 7 and identify its position.
  3. 3The 7 is in the thousands place, which means it represents 7 × 1,000 = 7,000.

Worked Example

Problem

Write the number 'two hundred thirty-six thousand, five hundred twelve' in standard form.

Solution

236,512

Solution

Explanation

  1. 1Break down the words into place values: 'two hundred thirty-six thousand' = 236,000.
  2. 2'five hundred twelve' = 512.
  3. 3Combine them: 236,000 + 512 = 236,512.
  4. 4Check by reading it back: two hundred thirty-six thousand, five hundred twelve.

Question

What is the value of the digit 5 in the number 158,429?

Show Answer
50,000
Show Solution
Solution
  1. 1Identify the position of the digit 5 by counting from right to left: 9 (ones), 2 (tens), 4 (hundreds), 8 (thousands), 5 (ten thousands), 1 (hundred thousands).
  2. 2The digit 5 is in the ten thousands place.
  3. 3Calculate its value: 5 × 10,000 = 50,000.

Question

Write 405,073 in expanded form.

Show Answer
400,000 + 5,000 + 70 + 3
Show Solution
  1. 1Identify each digit and its place value: 4 (hundred thousands), 0 (ten thousands), 5 (thousands), 0 (hundreds), 7 (tens), 3 (ones).
  2. 2Write each non-zero digit times its place value: 4 × 100,000 = 400,000, 5 × 1,000 = 5,000, 7 × 10 = 70, 3 × 1 = 3.
  3. 3Connect with plus signs, skipping any zeros: 400,000 + 5,000 + 70 + 3.

Tip

Remember: Place value is like a number's address system - each digit lives in its own special place that tells you exactly how much it's worth!