Seven-digit numbers

1Summary 重點摘要

1,000,000 = one million.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: The place value chartThe largest place of a seven-digit number is the millions place. Place 1,234,567 into the chart: 1 in the millions, 2 in the hundred-thousands, 3 in the ten-thousands, 4 in the thousands, 5 in the hundreds, 6 in the tens and 7 in the ones. Memorise this left-to-right order and reading and writing stay orderly. Grouping three digits with commas helps see the size: 1,234,567 has three groups, the first holding one digit, so it is a seven-digit number. Why does place value matter? Because the same digit means completely different values in different places: a 1 in the millions is one million, in the ones only one. A common error is miscounting the digits; group with commas first, then count group by group.
2. Step 2: Reading aloudRead a seven-digit number from the largest place: say the part above the thousands first, then the rest. In Chinese reading, 1,234,567 reads as one hundred twenty-three wan plus four thousand five hundred sixty-seven, the front group 123 giving the wan part and the remainder 4567 read within four digits. Why read by groups? Because reading splits at the wan level, and grouping first keeps the layers clear and the errors away. Check group by group while reading, missing none and repeating none. A common error is grouping wrongly, pulling too many digits into the front group; write the commas first, read each group in turn, then read the whole number once through as a check.
3. Step 3: Reading zerosZeros follow fixed rules: a run of zeros in the middle is spoken once, and zeros at the end are silent. 4,050,600 reads as four hundred five wan plus six hundred: after the 4 in the millions, the hundred-thousands and thousands are both 0, and the two zeros in the run are spoken just once, while the two zeros at the end are not read at all. Why must the middle zeros be read? Because zeros stand for empty places, and without reading them 4,050,600 and 4,500,600 would sound the same; reading the zero reports the gap. A common error is reading every zero in the run; the rule is one zero for the whole run, spoken where the run sits.
4. Step 4: Writing from wordsWriting a number from spoken words matches each part to its place: hearing seven hundred thousand and five hundred, put the 7 in the hundred-thousands place, fill the ten-thousands and thousands with 0, put the 5 in the hundreds, and pad the remaining places with 0, giving 700,500. Why pad with zeros? Because empty places must be held by 0, or every other digit shifts position; missing the padding turns the number into 7,500, entirely different. After writing, read it back and compare with the words, correcting any mismatch at once. A common error is too little padding or a misplaced digit; fill from the largest place downward using the chart, then read back to verify.
5. Step 5: Expanded formThe expanded form multiplies each digit by its place value and adds: 1,234,567 = 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7. The expansion displays what every digit is worth, deepens the understanding of place value, and doubles as a check on reading and writing: 700,500 = 700,000 + 500 shows at a glance that 7 sits in the hundred-thousands and 5 in the hundreds. A common error is a wrong place value, such as writing the 5 of the hundreds as 5,000; after expanding, match each term to the original digit by digit, and the terms must sum to the original number — if not, some place has been written wrongly.
6. Step 6: Comparing sizesTo compare sizes, look at the number of digits first: 999,999 is the largest six-digit number and 1,000,000 the smallest seven-digit number, so 1,000,000 > 999,999 — larger by just 1, yet a whole place larger. Why do more digits mean larger? Because the seven-digit number commands the millions place, which no six-digit number can reach. With equal digit counts, compare place by place from the left: whichever number first shows a larger digit is the larger one, and 4,050,600 against 4,500,600 is decided at the second digit. A common error is skipping places midway through the comparison; move left to right one place at a time and stop once the result appears.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Seven-digit numbers start at 1,000,000
• Place order: millions, hundred-thousands, ten-thousands, thousands, hundreds, tens, ones
• Group three digits with commas from the right
• Middle zeros are spoken; trailing zeros are silent
• Compare numbers: digit count first, then left to right