Convert decimals between standard and expanded form
Just like whole numbers, decimals can be 'stretched out' into expanded form to show the value of each digit. It's a great way to see the building blocks of a decimal number! 🧱
Concept
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.
Try it
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?