Grade 4 Large Numbers Practice

What this problem type covers

Thirteen problem types across five levels of reasoning: totalling counted notes and coins, adding in four-digit groups, reading a value between two ticks, finding which of several numbers is nearest, dividing by a place value, comparing two occurrences of the same digit, undoing a scaling, recovering the step of a count, counting the digits that satisfy an inequality, deciding a comparison the box cannot affect, intersecting two conditions, deducing a number from several clues, and building the smallest number from repeated cards.

Example problems

One example from each difficulty band, with worked solutions.

Questi esercizi sono generati automaticamente. Le risposte nascono insieme all’esercizio e sono verificate da test, ma possono esserci errori: segnalaceli.

1. 1 · ★1
   Work out 464,905,510,000 + 324,636,870,000.
   • ①789,442,380,000
   • ②789,542,380,000
   • ③789,542,390,000
   • ④789,642,380,000
   • ⑤789,542,370,000
   Show solution

   ②789,542,380,000

   1. Add in four-digit groups: the ten-thousands group and the hundred-millions group separately.
   2. The ten-thousands groups add to 4,238.
   3. That is below 10,000, so nothing is carried.
   4. The sum is 789,542,380,000.
2. 2 · ★2
   On a number line the space between 3,100,000,000 and 3,200,000,000 is divided into 5 equal parts. What number is 1 parts to the right of 3,100,000,000?
   • ①3,200,000,000
   • ②3,140,000,000
   • ③3,100,000,000
   • ④3,120,000,000
   • ⑤3,160,000,000
   Show solution

   ④3,120,000,000

   1. One large interval is 100,000,000.
   2. It is split into 5 equal parts, so one small interval is 20,000,000.
   3. Count on 1 small intervals of 20,000,000.
   4. The number is 3,120,000,000.
3. 3 · ★3
   6,411,552,000 multiplied by 100 equals some number multiplied by 100,000. Find that number.
   • ①6,411,552
   • ②641,155,200,000
   • ③641,155,200
   • ④6,411,552,000
   • ⑤64,115,520
   Show solution

   ①6,411,552

   1. 6,411,552,000 multiplied by 100 is 641,155,200,000.
   2. 641,155,200,000 is also some number multiplied by 100,000.
   3. Undo the 100,000 by removing 5 zeros from 641,155,200,000.
   4. The number is 6,411,552.
4. 4 · ★4
   How many of the digits 0 to 9 can go in the box?
   743,336 > 74□,336
   • ①5
   • ②4
   • ③2
   • ④7
   • ⑤3
   Show solution

   ⑤3

   1. Both numbers have the same number of digits, so compare from the highest place down.
   2. The digits match until the box, so the box decides the comparison.
   3. The digits that work are 0, 1, 2.
   4. That is 3 of them.
5. 5 · ★5
   Using each of the cards 0, 5, 9, 4 exactly twice, an eight-digit number is made. Find the smallest such number.
   • ①40,046,599
   • ②40,045,609
   • ③99,554,400
   • ④4,455,990
   • ⑤40,045,599
   Show solution

   ⑤40,045,599

   1. Each card is used twice, so the digits available are 0, 0, 4, 4, 5, 5, 9, 9.
   2. To make the smallest number, put the smallest digits in the highest places.
   3. A leading zero is not allowed, so the smallest non-zero digit goes first.
   4. The smallest number is 40,045,599.

Where people usually go wrong

• Counting coins at the wrong place value. 135 hundred-won coins are 13500, not 135000.
• Counting large ticks instead of small ones. If one interval of 10000000 is split into 4, each small tick is 2500000.
• Dividing by the ordinal instead of the number of jumps. From the 1st term to the 4th is three jumps, not four.
• Rounding up when exchanging for cheques. Money left below one million cannot become a cheque, so the whole-number part is the answer.
• Miscounting the places between two digits. Each step up is ten times, so four places apart is 10000 times, not 4.
• Including the digit that makes the two numbers equal. The question asks which digits make it strictly greater.
• Assuming a box makes a comparison undecidable. If no digit can win at that place, the next place settles it whatever the box holds.
• Leaving a zero in front when building the smallest number. The smallest non-zero digit has to lead.
• Stopping at the first digit that fits one clue. A clue narrows the possibilities; only all the clues together fix the number.