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Place Values in Decimal Numbers

Decimals continue the place value pattern beyond the ones place! Just like whole numbers, each decimal place is 10 times smaller than the place before it. Let's explore the world beyond the decimal point!

Lesson 4

Concept

Place value extends infinitely in both directions - the decimal point is just a marker! 🎯 **The Place Value System:** **Whole Numbers ← | → Decimals** Thousands | Hundreds | Tens | Ones . tenths | hundredths | thousandths Each step RIGHT ÷ 10 Each step LEFT × 10 📊 **Decimal Place Values:** In the number **3.475**: • 3 is in the **ones** place = 3 • 4 is in the **tenths** place = 4/10 = 0.4 • 7 is in the **hundredths** place = 7/100 = 0.07 • 5 is in the **thousandths** place = 5/1000 = 0.005 Total: 3 + 0.4 + 0.07 + 0.005 = 3.475 💡 **Understanding Decimal Places:** **TENTHS (one decimal place):** • The first place after the decimal point • 0.7 = 7/10 = 7 tenths • Think: dividing 1 into 10 equal parts **HUNDREDTHS (two decimal places):** • The second place after the decimal point • 0.45 = 45/100 = 45 hundredths • Think: dividing 1 into 100 equal parts **THOUSANDTHS (three decimal places):** • The third place after the decimal point • 0.328 = 328/1000 = 328 thousandths • Think: dividing 1 into 1,000 equal parts 🌟 **Reading Decimals:** **0.6** = "six tenths" or "zero point six" **0.34** = "thirty-four hundredths" or "zero point three four" **0.825** = "eight hundred twenty-five thousandths" or "zero point eight two five" **5.92** = "five and ninety-two hundredths" or "five point nine two" 🎨 **Expanded Form:** **2.365** can be written as: • 2 + 0.3 + 0.06 + 0.005 • (2 × 1) + (3 × 0.1) + (6 × 0.01) + (5 × 0.001) • 2 + 3/10 + 6/100 + 5/1000 **Visual Model:** Think of money! • Ones place = $1 bills • Tenths = dimes ($0.10) • Hundredths = pennies ($0.01) So 2.35 = 2 dollars + 3 dimes + 5 pennies = $2.35 📏 **The Pattern Continues:** ...thousands, hundreds, tens, ones . tenths, hundredths, thousandths... Each place is 1/10 of the place to its left! **Key Understanding:** The decimal point separates whole numbers from parts of a whole. To the left: whole numbers To the right: fractional parts

Try it

Practice identifying place values in decimals! 📝 **Identify the Place Value:** In the number 4.826: 1. What digit is in the tenths place? 2. What digit is in the hundredths place? 3. What digit is in the ones place? 4. What digit is in the thousandths place? 🎯 **What's the Value?** In 7.359: 5. What's the value of the 3? 6. What's the value of the 5? 7. What's the value of the 9? 8. What's the value of the 7? 💡 **Write in Expanded Form:** 9. 2.4 = ? 10. 5.73 = ? 11. 8.426 = ? 12. 12.805 = ? 📊 **Convert from Fractions:** 13. 6/10 = ? (as a decimal) 14. 42/100 = ? (as a decimal) 15. 538/1000 = ? (as a decimal) 🏆 **Write the Decimal:** 16. 3 ones, 5 tenths, 2 hundredths = ? 17. 8 and 47 hundredths = ? 18. 216 thousandths = ? 19. 9 ones, 0 tenths, 8 hundredths, 3 thousandths = ? 💪 **Reading Decimals:** 20. Write in words: 0.75 21. Write in words: 3.408 22. Write in words: 0.6 23. Write as a decimal: "forty-three hundredths" 24. Write as a decimal: "five and six tenths" 🎯 **Challenge:** 25. Which is larger: the 5 in 4.567 or the 5 in 3.254? How many times larger? 26. Create a decimal where: • 8 is in the tenths place • 2 is in the ones place • 6 is in the hundredths place 27. Explain why 0.5 = 0.50 = 0.500 (they're all the same value!)