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I.1 Place value models up to 1,000

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What is place value?

Place value is the value of a digit depending on where it is in a number. Each place (ones, tens, hundreds) shows how much the digit is worth.

Examples:
  • In 325: the 3 is in the hundreds place β†’ 300
  • The 2 is in the tens place β†’ 20
  • The 5 is in the ones place β†’ 5
Note

Each place to the left is worth 10 times more than the one before it.

How do you identify place value?

Look at the position of each digit in the number. The digit’s place tells you its value.

Steps:
  • Write the number: 748
  • Identify each digit’s place: 7 hundreds, 4 tens, 8 ones
  • Expand the number: 700 + 40 + 8
Note

You can break apart numbers using place value. This is called expanded form.

Building numbers up to 1,000

Numbers up to 1,000 are built using hundreds, tens, and ones. The largest three-digit number is 999.

Examples:
  • 256 = 2 hundreds + 5 tens + 6 ones
  • 903 = 9 hundreds + 0 tens + 3 ones
  • 470 = 4 hundreds + 7 tens + 0 ones
Note

A zero in a place means there are no groups of that value.

Comparing numbers by place value

Compare numbers by looking at the largest place first. Start with the hundreds, then tens, then ones.

Examples:
  • 482 is greater than 375 because 4 hundreds is greater than 3 hundreds.
  • 629 is less than 635 because the tens place (2 tens) is less than (3 tens).
Note

Always compare digits starting from the left. Stop when you find the first difference.

Using place value to add and subtract

You can use place value to help add and subtract by regrouping (borrowing or carrying) hundreds, tens, and ones.

Examples:
  • 37 + 25 β†’ add ones: 7 + 5 = 12 (regroup 10 as 1 ten and keep 2 ones) β†’ 62
  • 52 βˆ’ 19 β†’ subtract ones: 2 βˆ’ 9 (regroup 1 ten as 10 ones) β†’ 33
Note

Regrouping helps when the ones or tens are too large or too small to add or subtract easily.