What is the value of the digit in the hundred thousands place?
Place Value: The value of a digit depends on its position in the number. Each position represents a power of 10.
- Identify the place value positions from right to left: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions
- Locate the specified place value position
- Identify the digit in that position
- Calculate the value of that digit in its position
From right to left: Ones (1), Tens (10), Hundreds (100), Thousands (1,000), Ten Thousands (10,000), Hundred Thousands (100,000), Millions (1,000,000)
Counting from the right: 1(ones), 3(tens), 5(hundreds), 8(thousands), 2(ten thousands), 7(hundred thousands), 4(millions)
The digit in the hundred thousands place is 7
Value = Digit × Place Value = 7 × 100,000 = 700,000
The value of the digit in the hundred thousands place is 700,000
• Place Value Rule: Each position represents a power of 10
• Position Counting: Count positions from right to left starting with ones
• Value Calculation: Digit × Place Value = Actual Value
Expanded Form: Writing a number as the sum of the value of each digit based on its place value.
6 in millions (6 × 1,000,000 = 6,000,000)
4 in hundred thousands (4 × 100,000 = 400,000)
7 in ten thousands (7 × 10,000 = 70,000)
2 in thousands (2 × 1,000 = 2,000)
8 in hundreds (8 × 100 = 800)
5 in tens (5 × 10 = 50)
3 in ones (3 × 1 = 3)
6,472,853 = 6,000,000 + 400,000 + 70,000 + 2,000 + 800 + 50 + 3
Add all parts: 6,000,000 + 400,000 + 70,000 + 2,000 + 800 + 50 + 3 = 6,472,853 ✓
6,472,853 = 6,000,000 + 400,000 + 70,000 + 2,000 + 800 + 50 + 3
• Expanded Form Rule: Sum of each digit multiplied by its place value
• Place Value Recognition: Each position has a specific value
• Verification: Always check by adding the expanded parts
Number Comparison: Start comparing digits from the highest place value to the lowest until a difference is found.
Millions: 5 = 5 (equal)
Hundred Thousands: 2 = 2 (equal)
Ten Thousands: 8 = 8 (equal)
Thousands: 3 = 3 (equal)
Hundreds: 7 = 7 (equal)
Tens: 4 = 4 (equal)
Ones: 1 vs 9 (different!)
Since 1 < 9, we can conclude that 5,283,741 < 5,283,749
5,283,741 < 5,283,749
5,283,749 is greater than 5,283,741
• Comparison Rule: Start from the highest place value and move right
• First Difference Rule: The first differing digit determines the relationship
• Greater Than Rule: The larger digit in the first differing place makes the number greater
Definitions:
- Place Value: The value of a digit based on its position in the number
- Face Value: The actual value of the digit itself (ignoring position)
- Expanded Form: Writing a number as the sum of each digit multiplied by its place value
- Standard Form: Writing a number in its normal numeric form
- Word Form: Writing a number using words
Core Rules and Principles:
- Each place value is 10 times the previous one (tens = 10 × ones, hundreds = 10 × tens, etc.)
- Place value positions from right to left: ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions
- When comparing numbers, start from the highest place value and work right
- For rounding, look at the digit immediately to the right of the target place
Methods and Procedures:
- Place Value Identification: Count positions from right to left, identify digit, multiply by place value
- Expanded Form: Multiply each digit by its place value, add all products
- Number Comparison: Start from leftmost digit, compare until difference found
- Rounding: Look at digit to right of target place, ≥5 round up, <5 round down
Examples:
- In 3,456,789: the 4 is in hundred thousands place and has value 400,000
- Expanded form of 2,345: 2,000 + 300 + 40 + 5
- Comparing 4,567 and 4,576: since 6 < 7 in tens place, 4,567 < 4,576
Tips and Tricks:
- Use commas to separate periods (thousands, millions) for easier reading
- Remember: each place is 10 times the previous one
- When comparing, stop at the first different digit
- Zeros still hold place value positions
- For rounding, look at the digit immediately to the right of target place
Key Notes for Memorization:
- "Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions" - practice this sequence
- Always count place values from right to left
- When reading large numbers, break into groups: 3,456,789 is "three million, four hundred fifty-six thousand, seven hundred eighty-nine"
- Remember: place value ≠ face value
Effective Worksheet Completion Tips:
- Read Carefully: Understand what each question is asking before solving
- Use Visual Aids: Draw place value charts to organize digits
- Check Your Work: Always verify your answers by working backwards
- Work Systematically: Solve problems in order and show all steps
- Use Examples: Refer back to solved examples when stuck
Common Worksheet Mistakes:
- Confusing place value with face value
- Misreading large numbers due to missing commas
- Incorrectly identifying place value positions
- Making arithmetic errors in expanded form
- Not following rounding rules correctly
Self-Assessment Questions:
- Can I identify the place value of any digit in a number up to millions?
- Can I write numbers in expanded form accurately?
- Can I compare numbers up to millions correctly?
- Can I round numbers to any specified place value?
- Can I solve word problems involving place value?
- Identify positions: Remember the order from right to left
- Locate digit: Find the digit in the specified place
- Calculate value: Multiply the digit by its place value
- Compare systematically: From highest to lowest place value
• Position counting: Right to left starting with ones
• Value calculation: Digit × Place Value
• Comparison: Highest to lowest place value
• Expanded form: Sum of all place values
• Rounding: Look at the digit to the right of the target place
Rounding: Replacing a number with an approximate value that has a simpler representation.
We need to round to the nearest hundred thousand, so we focus on the hundred thousands place (7) and the digit to its right (ten thousands place, which is 2).
If the digit to the right of the target place is 5 or greater, round up. If less than 5, round down.
The digit in the ten thousands place is 2, which is < 5, so we round down.
The hundred thousands digit remains 7.
All digits to the right of the hundred thousands place become zeros: 4,700,000
4,728,531 is closer to 4,700,000 than to 4,800,000 because it's less than halfway between them.
4,728,531 rounded to the nearest hundred thousand is 4,700,000
• Rounding Rule: Look at the digit immediately to the right of the target place
• Round Up: If right digit ≥ 5, increase target digit by 1
• Round Down: If right digit < 5, keep target digit the same
Word Problem: A real-world scenario requiring mathematical reasoning and place value understanding.
Round 6,472,853 to the nearest million.
The millions place has the digit 6. The digit to its right (hundred thousands place) has the digit 4.
Since the digit to the right (4) is < 5, we round down, keeping the millions digit the same.
All digits to the right of the millions place become zeros: 6,000,000
The mayor should report 6,000,000 people.
6,472,853 is between 6,000,000 and 7,000,000. Since it's less than halfway (less than 6,500,000), it rounds down to 6,000,000.
The mayor should report 6,000,000 people
• Problem Analysis: Identify what place value to round to
• Rounding Application: Apply standard rounding rules
• Context Understanding: Interpret the result in the real-world context