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Decimals in expanded form

Decimals in expanded form

Decimals in expanded form represent a decimal number by breaking it down into the sum of its place values. Each digit is multiplied by its corresponding power of ten based on its position.

For example, in the decimal number 3.52:

  • The digit 3 is in the "ones" place, so it represents 3×13 \times 1
  • The digit 5 is in the "tenths" place, so it represents 5×0.15 \times 0.1
  • The digit 2 is in the "hundredths" place, so it represents 2×0.012 \times 0.01

Putting it all together, 3.52 in expanded form is:

3×1+5×0.1+2×0.013 \times 1 + 5 \times 0.1 + 2 \times 0.01

This format helps to clearly visualize the contribution of each digit to the overall value of the decimal.

In this article
Part 1: Write decimals in expanded form

Part 1: Write decimals in expanded form

To write a decimal in expanded form, we need to break down each digit according to its place value. Start with the whole number portion, identifying the hundreds, tens, and ones places. Then, move on to the tenths, hundredths, and thousandths places. Keep in mind the order of operations when combining the expanded terms.

When studying "Write decimals in expanded form," focus on these key points:

  1. Understanding Expanded Form: Recognize that expanded form expresses a number as the sum of its individual place values.

  2. Place Value System: Familiarize yourself with the place values of decimal numbers, including tenths, hundredths, thousandths, etc.

  3. Breaking Down the Number: Learn to break down each digit according to its place value. For example, in the decimal 4.56, break it into 4 (whole number) + 0.5 (five tenths) + 0.06 (six hundredths).

  4. Using Coefficients: Use coefficients multiplied by their respective place values to represent the digits (e.g., 4×14 \times 1, 5×0.15 \times 0.1, 6×0.016 \times 0.01).

  5. Combining Terms: Combine all the terms to construct the full expanded form.

  6. Practice with Examples: Practice with various decimal numbers to solidify understanding, ensuring to include both whole and fractional parts in the expanded form.

By mastering these points, you can efficiently write decimals in expanded form.

Related topics

Decimal place value intro

Decimals on the number line

Decimals in written form

Decimals in different forms

Comparing decimals

Rounding decimals

Part 1: Write decimals in expanded form