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!
Do this: Read the concept below, then try the quiz or activity.
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 place27. Explain why 0.5 = 0.50 = 0.500 (they're all the same value!)