Understanding Place Value

What is Place Value?

Place value tells us the value of a digit based on its position in a number. Each digit in a number has a different value depending on where it is.

For example, in the number 3,245:

  • The 3 is in the thousands place and is worth 3,000.
  • The 2 is in the hundreds place and is worth 200.
  • The 4 is in the tens place and is worth 40.
  • The 5 is in the units (or ones) place and is worth 5.

So, we can say:

$$3,245 = 3,000 + 200 + 40 + 5$$

Key Rules for Place Value

  1. Each place value is 10 times bigger than the place to its right.
  2. The rightmost digit is always the ones place.
  3. Moving left, the places are tens, hundreds, thousands, and so on.

Tips and Tricks

  • Use place value charts to help see where each digit goes.
  • Remember the rhyme: “Ones, Tens, Hundreds, Thousands!” to keep the order straight.

Understanding Decimals

What are Decimals?

Decimals are a way to show numbers that are less than one. They are written using a decimal point.

For example, in the number 3.5:

  • The 3 is in the ones place (or whole number part).
  • The 5 is in the tenths place (or decimal part).

Key Rules for Decimals

  1. The first digit after the decimal point is the tenths place.
  2. The second digit after the decimal point is the hundredths place.
  3. The third digit after the decimal point is the thousandths place.

Tips and Tricks

  • Use a number line to help understand where decimals fit between whole numbers.
  • Visual aids like base ten blocks can help show how decimals work.

Questions on Place Value and Decimals

Easy Level Questions

  1. What is the value of the digit 6 in the number 6,782?
  2. In the number 4.2, what is the value of the digit 2?
  3. What digit is in the tens place of 1,456?
  4. Write the number 3,210 in expanded form.
  5. What is the value of the digit 8 in 8,905?
  6. In the number 0.7, what place does the digit 7 occupy?
  7. What is the value of the digit 5 in the number 5,432?
  8. Write the number 2.5 in words.
  9. What digit is in the hundreds place of 2,639?
  10. What is the value of the digit 3 in 3.14?
  11. Write the number 1,000 in expanded form.
  12. What is the value of the digit 9 in the number 9,876?
  13. Identify the digit in the ones place in the number 7,321.
  14. What is the value of 4 in the number 4.56?
  15. Write the number 5,000 in words.
  16. What is the digit in the tenths place of 3.8?
  17. Write 2,345 in expanded form.
  18. Identify the digit in the thousands place in 4,567.
  19. What is the value of the digit 6 in the number 6.72?
  20. Write the number 0.4 in words.

Medium Level Questions

  1. What is the total value of the digits in the number 5,432?
  2. Write the number 0.35 in expanded form.
  3. In the number 7,890, what is the value of the digit 8?
  4. Write the number 3,405 in words.
  5. How many tenths are in the number 4.6?
  6. What digit is in the hundreds place of 9,234?
  7. Write the number 4,567 in expanded form.
  8. What is the value of the digit 9 in the number 9.01?
  9. Write the number 0.004 in expanded form.
  10. What is the value of the digit 2 in 12.45?
  11. Identify the digit in the tenths place of 2.89.
  12. What is the value of the digit 5 in the number 5,123?
  13. Write the number 1.25 in words.
  14. What digit is in the thousands place of 3,276?
  15. Write 6,789 in expanded form.
  16. What is the value of the digit 4 in the number 24.56?
  17. Identify the digit in the ones place of 0.9.
  18. Write the number 7.5 in expanded form.
  19. What digit is in the thousands place of 8,341?
  20. What is the value of the digit 3 in 3,456?

Hard Level Questions

  1. Write the number 52,307 in expanded form.
  2. What is the total value of the digits in the number 4.56?
  3. Write the number 0.0057 in words.
  4. What is the digit in the hundredths place of 6.789?
  5. Write the number 9,876 in expanded form.
  6. What is the value of the digit 7 in the number 7,543?
  7. Identify the digit in the thousands place of 19,282.
  8. What is the value of the digit 3 in 3.14159?
  9. Write 0.09 in expanded form.
  10. What is the digit in the tenths place of 4.567?
  11. Write the number 1,234.56 in words.
  12. Identify the digit in the ones place of 0.02.
  13. Write the number 76,543 in expanded form.
  14. What is the total value of the digits in the number 5.67?
  15. Write the number 2.005 in words.
  16. What is the value of the digit 8 in the number 8,765.43?
  17. Identify the digit in the hundredths place of 5.678.
  18. What is the value of the digit 1 in 1,234.56?
  19. Write the number 0.123 in expanded form.
  20. Identify the digit in the thousands place of 12,345.

Answers

Easy Level Answers

  1. 6000
  2. 0.2
  3. 4
  4. 3,000 + 200 + 10 + 0
  5. 9000
  6. Tenths
  7. 5000
  8. Two point five
  9. 2
  10. 0.03
  11. 1,000
  12. 900
  13. 1
  14. 0.04
  15. Five thousand
  16. 8
  17. 2000 + 300 + 40 + 5
  18. 4
  19. 0.6
  20. Zero point four

Medium Level Answers

  1. 5000 + 400 + 30 + 2
  2. 0.30 + 0.05
  3. 800
  4. Three thousand four hundred five
  5. 46
  6. 2
  7. 4000 + 500 + 60 + 7
  8. 0.9
  9. 0.004 + 0.0007
  10. 2
  11. 8
  12. 5000
  13. One point two five
  14. 3
  15. 6,000 + 700 + 80 + 9
  16. 0.04
  17. 0.7
  18. 0.04
  19. 7000 + 500 + 70 + 5
  20. 3

Hard Level Answers

  1. 50,000 + 2,000 + 300 + 7
  2. 4 + 0.5 + 0.06
  3. Zero point zero zero five seven
  4. 7
  5. 9000 + 800 + 70 + 6 + 0.03
  6. 7000
  7. 1
  8. 3
  9. 0.1 + 0.02 + 0.003
  10. 5
  11. One thousand two hundred thirty-four point five six
  12. 0
  13. 70,000 + 6,000 + 500 + 40 + 3
  14. 5 + 0.6 + 0.07
  15. Two point zero zero five
  16. 8000
  17. 6
  18. 1
  19. 0.1 + 0.02 + 0.003
  20. 12

Feel free to use this guide to learn more about place value and decimals! Happy learning!