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How Do You Write a Whole Number Given in Words in Standard Form and in Expanded Form?

Write 'nine hundred seventy thousand, four hundred eighty-two' in standard form and expanded form.

Summary

  1. Standard form is usually how you see numbers written
  2. A period is made up of 3 places, starting with the ones place and moving left
  3. Periods are named by their smallest place value
  4. Commas separate periods both when the number is written in words and in standard form
  5. Fill in the blanks by reading each period separately
  6. To write a number in expanded form, we add together the actual values of each digit in the number
  7. Adding the values in expanded form gives you the standard form of the number

Notes

    1. The comma separates our number into a few different chunks
    2. We can look at each of these chunks separately to figure out how to write our number in standard form
    1. Don't get confused -- here a 'period' isn't talking about a dot at the end of a sentence!
    2. 'Periods' are groups of 3 digits in a large number
    3. Periods are named by their smallest place value
    4. So the ones, tens and hundreds places make up the 'ones period'
    1. Commas separate periods both in standard form and in numbers written in words
    2. When a number is written in words, we say the name of the period right before the comma for everything except the ones period
    1. The millions period has the millions, ten-millions and hundred-millions places
    1. The ones, tens and hundreds places make up the ones period
    1. The thousands, ten-thousands and hundred-thousands make up the thousands period
    2. Notice that in the thousands period, we have 'thousand' at the end of every place value name
    1. Our largest place is the hundred-thousands place
    2. It has six spaces, so our number will have six spaces
    1. Go from left to right, like you read a book
    2. Put the digit of 9 in the hundred-thousands place
    1. When we get to the word 'thousand', that means that we're done with that period
    2. We just have 'seventy' before the 'thousand', so we just fill in the 7 and 0 for 70
    3. If we had something like 'seventy-two thousand', we would fill in a 7 and 2 for 72 instead
    1. The comma goes in the same place in the number in standard form as it does in words
    2. The ones period has the ones, tens and hundreds places
    1. Put the digit of 4 in the hundreds place
    1. Now our number is in standard form!
    1. We want to work our way from left to right
    1. The digit of 9 is in the hundred-thousands place
    2. That means the actual value of that 9 is 9 hundred-thousands, which we can write as 9•100,000
    1. In expanded form, we break down the number by finding the actual value of each digit and adding them together
    2. So to find the actual value of a digit, we just multiply it by its place value
    1. 7 is in the ten-thousands place, so we have 7 •10,000
    2. 0 is in the one-thousands place, so we have 0•1,000
    3. 4 is in the hundreds place, so we have 4•100
    4. 8 is in the tens place, so we have 8•10
    5. 2 is in the ones place, so we have 2•1
    1. Numbers that start with 1 and are followed by a bunch of zeros are powers of 10
    2. To multiply a number by a power of 10, just replace the 1 with that number!
    1. Expanded form is an addition problem
    2. All we're doing is adding together the actual values of each digit in a number
    1. Adding the values in expanded form gives you the standard form of the number
    2. This addition problem is really easy, since in each column we've only got one number that's not zero!