GoalWrite 5- and 6-digit numbers in standard and expanded form and put them in order.
New words
standard form · the usual way to write a number with digitsorder · put numbers in a line from the least to the greatest, or the other way roundleast · the smallest
Explanation
Standard form is the usual way to write a number with digits, such as 73,846. We say it: seventy-three thousand, eight hundred forty-six. Expanded form shows the value of each digit: 73,846 = 70,000 + 3,000 + 800 + 40 + 6. To put numbers in order, count the digits first. A number with more digits is greater, so any 6-digit number is greater than any 5-digit number. If two numbers have the same number of digits, compare them from the left, place by place, until the digits are different. A place value mat helps to line up the places.
Number
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
73,846
7
3
8
4
6
Worked examples
Standard form
Expanded form
48,052
40,000 + 8,000 + 50 + 2
48,205
40,000 + 8,000 + 200 + 5
480,250
400,000 + 80,000 + 200 + 50
Write three numbers in expanded form. 48,052 = 40,000 + 8,000 + 50 + 2. 48,205 = 40,000 + 8,000 + 200 + 5. 480,250 = 400,000 + 80,000 + 200 + 50. A zero in a place means that place adds nothing, so we leave it out.
Number
Hundred thousands
Ten thousands
Thousands
Hundreds
Tens
Ones
48,205
4
8
2
0
5
48,052
4
8
0
5
2
Compare 48,205 and 48,052. Both have 5 digits. The ten thousands are 4 and 4, the thousands are 8 and 8, and the hundreds are 2 and 0. Since 2 hundreds are more than 0 hundreds, 48,205 > 48,052.
1st (least)
2nd
3rd
4th (greatest)
48,052
48,205
408,520
480,250
Order 480,250; 48,205; 408,520 and 48,052 from the least to the greatest. The two 5-digit numbers come first: 48,052 and 48,205. Of the two 6-digit numbers, 408,520 has 0 ten thousands and 480,250 has 8 ten thousands. The order is 48,052; 48,205; 408,520; 480,250.
Class activity
Number card race. Write six numbers with 5 or 6 digits on cards, such as 91,430 and 190,430, and mix them up. Race to put them in order from the least to the greatest. Then read each number aloud and write it in expanded form.
Practice
1
Write 62,507 in expanded form.
60,000 + 2,000 + 500 + 7.
2
Write 600,000 + 5,000 + 90 + 4 in standard form.
605,094.
3
Which is greater, 91,430 or 190,430? Why?
190,430. It has 6 digits and 91,430 has only 5.
4
Order from the least to the greatest: 52,716; 52,176; 521,076; 51,999.
51,999; 52,176; 52,716; 521,076.
5
Mostafa wrote 80,000 + 400 + 7 as 84,007. Is he right?
No. The 4 is 4 hundreds, not 4 thousands, so the number is 80,407.