Ordering Whole Numbers

Show your work for each problem.

1.
Which list is in ascending order (from least to greatest)?
1. a)345; 15,600; 2,180; 102,000
2. b)102,000; 15,600; 2,180; 345
3. c)2,180; 345; 15,600; 102,000
4. d)345; 2,180; 15,600; 102,000
Answer: 345; 2,180; 15,600; 102,000
The numbers have 3, 4, 5 and 6 digits, so the order is $345 < 2{,}180 < 15{,}600 < 102{,}000$ . The other lists either start with the largest number or swap two numbers.
2.
Order these numbers from least to greatest: $5{,}408$ , $987$ , $12{,}300$ , $76$ . Which number comes second?
Answer: 987
The numbers have 2, 3, 4 and 5 digits: $76 < 987 < 5{,}408 < 12{,}300$ . The second number is $987$ .
3.
Which number is the largest?
1. a) $100{,}099$
2. b) $99{,}999$
3. c) $98{,}765$
4. d) $102{,}345$
Answer: $102{,}345$
$98{,}765$ and $99{,}999$ have only 5 digits. Of the two 6-digit numbers, $102{,}345$ has 2 thousands and $100{,}099$ has 0, so $102{,}345$ is the largest.
4.
Order from least to greatest: $3{,}402$ , $87$ , $21{,}050$ , $609$
Answer: $87 < 609 < 3402 < 21\,050$
1. Which number has the fewest digits? 87
2. Which number has 3 digits and comes next? 609
3. Which number comes third? (write the number without spaces or commas) 3402
4. Which number is the largest? (write the number without spaces or commas) 21050
5.
Put these mountain heights in descending order: Mount Fuji $3{,}776$ m, Aconcagua $6{,}961$ m, Matterhorn $4{,}478$ m. Which height is in the middle? (write the number without spaces or commas)
Answer: 4478
The thousands digits are 6, 4 and 3, so $6{,}961 > 4{,}478 > 3{,}776$ . The Matterhorn ( $4{,}478$ m) is in the middle.
6.
Use each of the digits 4, 9, 1 and 7 exactly once. What is the largest four-digit number you can make? (write the number without spaces or commas)
Answer: 9741
Write the digits in descending order: 9, 7, 4, 1. The largest number is $9{,}741$ .
7.
Order from least to greatest: $5{,}050$ , $5{,}005$ , $5{,}500$
Answer: $5005 < 5050 < 5500$
1. All three numbers have 4 digits and 5 thousands. What is the hundreds digit of $5{,}500$ ? 5
2. The other two numbers have 0 hundreds. Which of them is smaller? (write the number without spaces or commas) 5005
3. Which number is in the middle? (write the number without spaces or commas) 5050
8.
Which list is correctly written in descending order?
1. a) $47{,}305 > 47{,}350 > 47{,}035$
2. b) $47{,}350 > 47{,}305 > 47{,}035$
3. c) $47{,}035 > 47{,}305 > 47{,}350$
4. d) $47{,}350 > 47{,}035 > 47{,}305$
Answer: $47{,}350 > 47{,}305 > 47{,}035$
$47{,}035$ has 0 hundreds, so it is the smallest. $47{,}350$ and $47{,}305$ both have 3 hundreds; the tens decide: $5 > 0$ . So $47{,}350 > 47{,}305 > 47{,}035$ .
9.
Four players finished a game with these scores: Mia $86{,}420$ , Leo $86{,}240$ , Sara $86{,}402$ , Tom $84{,}620$ . Which score is in second place (the second largest)? (write the number without spaces or commas)
Answer: 86402
Tom has only 4 thousands, so he is last. Mia and Sara have 4 hundreds, Leo has 2. Mia has 2 tens, Sara 0. Descending: $86{,}420 > 86{,}402 > 86{,}240 > 84{,}620$ . Second place: $86{,}402$ .
10.
Use each of the digits 6, 0, 3 and 8 exactly once to make the smallest four-digit number.
Answer: 3068
1. Which of the four digits is the smallest? 0
2. A four-digit number cannot start with 0. Which digit goes in the thousands place? 3
3. Put the remaining digits in ascending order after it. What is the smallest number? (write the number without spaces or commas) 3068
11.
Put $7{,}090$ , $7{,}009$ , $7{,}900$ and $7{,}099$ in ascending order. Which number is third?
1. a) $7{,}900$
2. b) $7{,}099$
3. c) $7{,}090$
4. d) $7{,}009$
Answer: $7{,}099$
$7{,}900$ is the largest (9 hundreds). The other three have 0 hundreds: $7{,}009$ has 0 tens, $7{,}090$ and $7{,}099$ have 9 tens, and the ones decide. Order: $7{,}009 < 7{,}090 < 7{,}099 < 7{,}900$ . The third number is $7{,}099$ .
12.
Rank these cities by population from greatest to least: Madrid about $3{,}332{,}000$ , Rome about $2{,}755{,}000$ , Berlin about $3{,}782{,}000$ , Paris about $2{,}103{,}000$ .
Answer: $3\,782\,000 > 3\,332\,000 > 2\,755\,000 > 2\,103\,000$
1. All four populations have 7 digits. Which population is the largest? (write the number without spaces or commas) 3782000
2. Which population is in second place? 3332000
3. Which population is in third place? 2755000
4. Which population is the smallest? 2103000
13.
Rank these mountains from highest to lowest: Aconcagua $6{,}961$ m, Vinson $4{,}892$ m, Kilimanjaro $5{,}895$ m, Puncak Jaya $4{,}884$ m.
Answer: $6961 > 5895 > 4892 > 4884$
1. Which height is the greatest? (write the number without spaces or commas) 6961
2. Which height comes next? 5895
3. Two heights start with 48. Compare their tens: which one is higher? 4892
4. Which height is the lowest? 4884
14.
Use each of the digits 5, 0, 2, 7 and 0 exactly once. What is the smallest five-digit number you can make? (write the number without spaces or commas)
Answer: 20057
In ascending order the digits are 0, 0, 2, 5, 7. The number cannot start with 0, so 2 goes first, then 0, 0, 5, 7: $20{,}057$ .
15.
Order from greatest to least: $1{,}203{,}450$ , $1{,}230{,}450$ , $1{,}203{,}540$ , $1{,}230{,}045$
Answer: $1\,230\,450 > 1\,230\,045 > 1\,203\,540 > 1\,203\,450$
1. All four numbers start with 1 million and 2 hundred thousands. In which place do they first differ? Type its value (for example 1000 for thousands). 10000
2. Which number is the largest? (write the number without spaces or commas) 1230450
3. Which number is second? 1230045
4. Which number is the smallest? 1203450
16.
A stadium had these crowds on four match days: $48{,}095$ , $48{,}509$ , $48{,}950$ , $48{,}059$ . Put them in ascending order.
Answer: $48\,059 < 48\,095 < 48\,509 < 48\,950$
1. All four numbers start with 48. What is the smallest hundreds digit among them? 0
2. Two numbers have 0 hundreds. Which of them is smaller? (write the number without spaces or commas) 48059
3. Which number is second smallest? 48095
4. Which number is the largest? 48950
17.
You have the digit cards 3, 8, 0, 6 and 1. Using every card once, how much larger is the largest five-digit number than the smallest five-digit number?
Answer: 75942
1. What is the largest five-digit number? (write the number without spaces or commas) 86310
2. What is the smallest five-digit number? 10368
3. What is $86{,}310 - 10{,}368$ ? 75942
18.
These numbers are in ascending order: $405{,}060 < \square < 450{,}600 < 456{,}000$ . Which number can go in the box?
1. a) $450{,}660$
2. b) $400{,}560$
3. c) $460{,}500$
4. d) $405{,}600$
Answer: $405{,}600$
$405{,}600 > 405{,}060$ (6 hundreds against 0) and $405{,}600 < 450{,}600$ (0 ten thousands against 5). $400{,}560$ is too small, $450{,}660$ and $460{,}500$ are too large.