Convert decimals between standard and expanded form

Standard form is the way we normally write numbers (e.g., 2.35). Expanded form breaks down the number to show the value of each individual digit.

From Standard to Expanded Form

Let's break down the number 4.672.
*   The 4 is in the ones place, so its value is 4.
*   The 6 is in the tenths place, so its value is 0.6.
*   The 7 is in the hundredths place, so its value is 0.07.
*   The 2 is in the thousandths place, so its value is 0.002.

You can write this in two main ways:

1.  Decimal Expanded Form:
    4.672 = 4 + 0.6 + 0.07 + 0.002

2.  Fraction Expanded Form:
    4.672 = 4 + 6/10 + 7/100 + 2/1000

From Expanded to Standard Form

This is even easier! Just add the values together, making sure to line up the decimal points.

Problem: Write 8 + 0.2 + 0.09 in standard form.
*   Line them up:
      8.00
      0.20
    + 0.09
    ------
      8.29
*   The standard form is 8.29.

Problem: Write 5 + 3/10 + 4/1000 in standard form.
*   5 is the whole number.
*   3/10 means a 3 in the tenths place.
*   4/1000 means a 4 in the thousandths place.
*   We need a placeholder zero in the hundredths place.
*   Result: 5.304

Key Idea: Expanded form makes it clear that a digit's value depends entirely on its place relative to the decimal point.

Practice with standard and expanded form!

Standard to Expanded Form (Decimal): 1. 5.42 = ? 2. 12.08 = ? 3. 0.789 = ?

Standard to Expanded Form (Fraction): 4. 6.3 = ? 5. 9.25 = ? 6. 2.047 = ?

Expanded to Standard Form: 7. 3 + 0.1 + 0.04 = ? 8. 10 + 0.5 + 0.006 = ? 9. 7 + 2/10 + 8/100 = ? 10. 4/10 + 9/1000 = ? (Be careful with placeholders!)

Word Problems: 11. A beetle is 2.45 cm long. Write its length in expanded form using fractions. 12. The result of a science experiment was 10 + 0.07 + 0.009. Write this result in standard form.

Challenge Problems: 13. Write 50.602 in two different expanded forms. 14. What number has a 4 in the tens place, a 3 in the tenths place, and a 6 in the thousandths place?