Every digit in a number has a place, and each place has a value. In a number like 34,516 there are five digits and five columns: ten thousands, thousands, hundreds, tens and ones. Reading from the right, each column is worth ten times more than the one before it: 1 one, 10 tens, 100 hundreds, 1,000 thousands, 10,000 ten thousands.
The value of a digit is not just the digit itself, it is the digit multiplied by its column. In 34,516 the 3 is not worth 3, it is worth 3 ten thousands, or 30,000, because of where it sits.
Expanded form breaks a number apart into the value of each of its digits, added together. It shows exactly what a number is made of.
Write the value of the digit shown in bold in each number.
Complete the table. Fill in the missing standard form, word form or expanded form for each number.
| Standard form | Word form | Expanded form |
|---|---|---|
| 23,450 | ||
| forty-one thousand, six hundred and seventeen | ||
| 60,000 + 5,000 + 300 + 9 | ||
| 30,082 | ||
| seventeen thousand, two hundred and five |
To compare two numbers, first look at how many digits each one has. A number with more digits is always bigger, as long as neither number starts with a zero. If both numbers have the same number of digits, compare them column by column, starting from the digit with the highest place value on the left.
Find the first column where the digits are different. Whichever number has the bigger digit in that column is the bigger number, no matter what the digits after it are. The symbols < and > show the comparison: the open end of the symbol always faces the bigger number.
To order a list of numbers, use the same method to compare them, one pair at a time, until the whole list is in order.
Circle the correct symbol to compare each pair of numbers.
Write each set of numbers in the order asked for.
Rounding makes a number simpler while keeping it close to its actual value. To round a number to the nearest 1000, look only at the hundreds digit, the digit straight after the thousands digit.
If the hundreds digit is 5, 6, 7, 8 or 9, round up: add 1 to the thousands digit and change every digit after it to zero. If the hundreds digit is 0, 1, 2, 3 or 4, round down: keep the thousands digit the same and change every digit after it to zero.
Mark 27,850 on the number line below to help you round it. Then round each number to the nearest 1000 and match it to its correct rounded value, writing the matching letter next to each number.
For the parent or supervisor: set this page aside before handing over the worksheet.
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