Reading and Writing Numbers up to 10,000,000

Reading and Writing Numbers up to 10,000,000

Standard Form

• Represents numbers using digits.
• Example: 3,245,678 is written as 3,245,678 in standard form.

Expanded Form

• Breaks down a number into its individual place values.
• Example: 3,245,678 = 3,000,000 + 200,000 + 40,000 + 5,000 + 600 + 70 + 8.

Place Value

• Each digit in a number has a specific value based on its position.
• Positions from right to left for 3,245,678:
  • 8 is in the ones place (10^0)
  • 7 is in the tens place (10^1)
  • 6 is in the hundreds place (10^2)
  • 5 is in the thousands place (10^3)
  • 4 is in the ten thousands place (10^4)
  • 2 is in the hundred thousands place (10^5)
  • 3 is in the millions place (10^6)

Number Comparison

• Compare numbers by examining their place values from left to right.
• Larger digits in higher place values signify larger numbers.
• Example: 3,245,678 > 3,145,678 because 2 > 1 in the hundred thousands place.

Number Rounding

• Adjusts the number to the nearest specified place value.
• Rules:
  • If the digit to the right is 5 or greater, round up.
  • If the digit is less than 5, round down.
• Example: Rounding 3,245,678 to the nearest thousand:
  • Look at the hundreds place (6): 3,245,678 rounds to 3,246,000.

Standard Form

• Utilizes digits exclusively to represent numbers.
• Example: 3,245,678 is expressed simply as 3,245,678.

Expanded Form

• Decomposes a number into its constituent place values.
• Example breakdown: 3,245,678 = 3,000,000 + 200,000 + 40,000 + 5,000 + 600 + 70 + 8.

Place Value

• Each digit's value is determined by its position in the number.
• Position analysis for 3,245,678 (right to left):
  • 8: ones place (10^0)
  • 7: tens place (10^1)
  • 6: hundreds place (10^2)
  • 5: thousands place (10^3)
  • 4: ten thousands place (10^4)
  • 2: hundred thousands place (10^5)
  • 3: millions place (10^6)

Number Comparison

• Analyze numbers by evaluating place values sequentially from left to right.
• Higher digits in earlier places indicate larger numbers.
• Example: 3,245,678 is greater than 3,145,678 due to 2 (hundred thousands) being greater than 1.

Number Rounding

• A method for estimating a number to the closest specified place value.
• Rounding rules:
  • If the next digit is 5 or greater, round up.
  • If the next digit is less than 5, round down.
• Example of rounding: For 3,245,678, the hundreds place (6) prompts a round up to 3,246,000 when rounding to the nearest thousand.