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Mastering Expanded Form: A Simple Guide to Understanding and Applying the Concept

To help solidify your understanding of expanded form, we’ve created downloadable flashcards and an instructional video. These resources provide additional practice and reinforce the concepts explained in the Khan Academy video.

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Understanding Expanded Form: Step-by-Step Guide

Breaking Down a Number

To write a number in expanded form, you need to understand the value of each digit based on its position. Let’s take the number 14,897 as an example.

  1. Identify the Place Values7 is in the ones place.
    9 is in the tens place.
    8 is in the hundreds place.
    4 is in the thousands place.
    1 is in the ten-thousands place.

  2. Express Each Digit with its Place Value7 ones is simply 7.
    9 tens means 9 × 10, which equals 90.
    8 hundreds translates to 8 × 100, which equals 800.
    4 thousands means 4 × 1,000, which equals 4,000.
    1 ten-thousand translates to 1 × 10,000, which equals 10,000.

  3. Combine All ComponentsYou can express the number as the sum of its parts: 10,000 + 4,000 + 800 + 90 + 7.
    Alternatively, you can write it as: 1 × 10,000 + 4 × 1,000 + 8 × 100 + 9 × 10 + 7 × 1.

Visualizing the Concept

To make this clearer, imagine each digit as a different colored poker chip, where each color represents a different place value. For example, one blue poker chip might represent 10,000, four green chips represent 1,000 each, and so on.


Applying Expanded Form

By practicing this breakdown process, you’ll get better at recognizing and writing numbers in expanded form. It helps to reinforce place value understanding, which is crucial for more advanced math concepts.

Remember, you can always refer back to our flashcards or instructional video for further practice and reinforcement. Mastering expanded form is a fundamental skill that will enhance your overall number sense and mathematical abilities.

When learning about writing numbers in expanded form, one of the best online resources is Khan Academy. Their clear and concise explanations make complex topics much easier to understand. Check out their video on expanded form for an in-depth lesson.

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