Four-digit numbers

1Summary 重點摘要

1000 to 9999. Thousands, hundreds, tens, ones.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Part 1: Four places from the rightTo read a four-digit number, start from the right: ones, tens, hundreds, and thousands; the order of the four places never changes. Why start from the right? The ones place is the anchor, and every place value grows from it toward the left. For 3456, the ones digit is 6, tens is 5, hundreds is 4, thousands is 3, read as three thousand four hundred fifty-six. Take care not to count the places from the left, which swaps ones with thousands and turns the number into something completely different.
2. Part 2: Same digit, different valueThe same digit can stand for different values in different places, and this is the core idea of place value. In 3456, the digit 4 is in the hundreds place, so it means 400, not 4. Why does position change value? Each place carries a fixed multiplier, a thousandfold in the thousands place and a hundredfold in the hundreds. Place value says: the digit is worth whatever its place makes it. Take care not to read the digits one by one in isolation; the 4 in 3456 is read as four hundred, not as a bare 4.
3. Part 3: Expanded formExpanded form breaks a number into the value of each place and adds them back, a fine tool for understanding place value. In 3456, the 3 thousands are 3000, the 4 hundreds are 400, the 5 tens are 50, and the 6 ones are 6, so 3456 = 3000 + 400 + 50 + 6. The expansion equals the original number exactly, only written differently. The usual error is dropping a place, leaving out the 50 for instance, which shortens the expansion; every place must appear, whatever its digit, with none left out.
4. Part 4: How big is 1000?Ten hundreds make 1000, the rate between the thousands and hundreds places. Try 999 + 1: the ones 9 + 1 makes 10, so write 0 and carry 1 to the tens; the tens and hundreds carry too, and the thousands digit becomes 1, giving 1000. One thousand is only 1 more than 999. Take care that 999 is the biggest three-digit number and 1000 the smallest four-digit one; they are neighbours with no whole number between, useful knowledge for estimating and for counting.
5. Part 5: Compare from the highest placeTo compare two four-digit numbers, look at the thousands first; if they are the same, look at the hundreds, then the tens and ones, always from the highest place down. Why start at the thousands? Differences there are the biggest and decide the comparison most. For 3456 and 3546, the thousands are both 3; in the hundreds, 4 is less than 5, so 3456 is less than 3546, and the lower places need no more looking. Take care that no matter how big the lower digits are, they cannot overturn the gap made higher up; once the hundreds decide, the tens and ones can be ignored, which makes comparing fastest.
6. Part 6: Carrying and zeros in the middleCount on from 1998: 1998, 1999, 2000; the last two digits change from 99 to 00 and the thousands digit from 1 to 2, an example of carrying all the way through. When reading, say the zeros in the middle too: 2005 is read as two thousand and five, and the zero may not be skipped. Take care that a middle zero, skipped in reading or in writing, shrinks the number; read 2005 without its middle zero and it becomes 205, a completely different value. The 0 holds a place, it belongs to the number, and it must be kept.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Four-digit numbers have thousands, hundreds, tens and ones, counted from the right
• 3456 = 3000 + 400 + 50 + 6
• The same digit has different values in different places
• Compare numbers place by place, starting from the thousands
• Always write and read zeros in the middle, e.g. 5070 is five thousand and seventy