Rounding · applications

Applications: Rounding

10 question types · Primary 4 · each worked step by step with a figure that follows the steps

PSLE · GCSE Higher

01

A Crowd Reported to the Nearest Hundred

strategyNumber Line / Find the Halfway Number on Each Side

A newspaper says that about 3400 people watched a football match. The number was rounded to the nearest hundred. (a) What is the smallest possible number of people? (b) What is the largest possible number of people?

330034003500
Each small mark is 10. The numbers nearest to 3400 round to 3400.
Mark 3400 on a number line, with 3300 and 3500 on either side.
step 1 of 5

Draw a number line with 3400 in the middle and the hundreds on either side. The numbers that round to 3400 start at one halfway number and stop just before the next.

  1. Mark 3400 on a number line, with 3300 and 3500 on either side.
  2. Halfway between 3300 and 3400 is 3350. A halfway number rounds up, so 3350 rounds to 3400. The number before it, 3349, rounds down to 3300.
  3. (a) The smallest possible number of people is 3350.
  4. Halfway between 3400 and 3500 is 3450. It rounds up to 3500, so the largest number that still rounds to 3400 is one less: 3450 − 1 = 3449.
  5. (b) The largest possible number of people is 3449.

answer(a) 3350; (b) 3449

techniqueRounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Giving 3450 as the largest number. 3450 is a halfway number, and a halfway number rounds up, so 3450 rounds to 3500.
  • Giving 3400 as the smallest number. Numbers below 3400 can round up to it. The smallest of them is the halfway number 3350.
02

One Number Rounded to the Nearest Ten and to the Nearest Hundred

strategyStart from the Original Number Each Time / One Digit Decides

A library has 3849 books. (a) Round 3849 to the nearest ten. (b) Round 3849 to the nearest hundred.

3840384538503849
Between 3840 and 3850, each mark is 1. The ones digit of 3849 is 9.
For the nearest ten, look at the ones digit. 3849 is between 3840 and 3850. The ones digit is 9, so round up.
step 1 of 5

Each rounding starts from the original number. For the nearest ten the ones digit decides. For the nearest hundred the tens digit decides.

  1. For the nearest ten, look at the ones digit. 3849 is between 3840 and 3850. The ones digit is 9, so round up.
  2. (a) To the nearest ten, 3849 is 3850.
  3. For the nearest hundred, go back to 3849. It is between 3800 and 3900, and the halfway number is 3850.
  4. The tens digit of 3849 is 4, so 3849 is less than 3850. Round down.
  5. (b) To the nearest hundred, 3849 is 3800. Check: 3849 is 49 from 3800 and 51 from 3900, so 3800 is nearer.

answer(a) 3850; (b) 3800

techniqueRounding to the Nearest Ten · Rounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding the rounded number: taking 3850 from part (a) and rounding it to 3900. Always start again from 3849, which is less than the halfway number 3850.
  • Looking at the ones digit 9 when rounding to the nearest hundred. For the nearest hundred the tens digit decides, and the tens digit is 4.
03

A Shopping Total Estimated by Rounding Each Price

strategyRound Each Price to the Nearest Ten Dollars / Compare the Estimate with the Exact Total

Mrs Tan buys a bag for $47, a shirt for $33 and a pair of shoes for $68. She rounds each price to the nearest ten dollars to estimate the total. (a) What is her estimate? (b) How many dollars more than the exact total is her estimate?

Real prices$47$33$68Rounded$50$30$70
$47 rounds up to $50, $33 rounds down to $30 and $68 rounds up to $70.
Round each price to the nearest ten dollars. $47 rounds up to $50, $33 rounds down to $30 and $68 rounds up to $70.
step 1 of 4

Round each price to the nearest ten dollars and add the rounded prices. Then add the real prices and compare the two totals.

  1. Round each price to the nearest ten dollars. $47 rounds up to $50, $33 rounds down to $30 and $68 rounds up to $70.
  2. (a) Her estimate is 50 + 30 + 70 = $150.
  3. Add the real prices to find the exact total: 47 + 33 + 68 = $148.
  4. (b) Her estimate is 150 − 148 = $2 more than the exact total. Check: rounding added $3 and $2 and took away $3, and 3 + 2 − 3 = 2.

answer(a) $150; (b) $2

techniqueRounding to the Nearest Ten · Rounding to Estimate

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding every price up. $33 is nearer to $30 than to $40, so it rounds down.
  • Saying the estimate and the exact total are the same. Two prices were rounded up by $5 altogether and one was rounded down by only $3, so the estimate is a little more.
04

Buses for a School Trip

strategyEstimate, Then Test / Round Up So That Everyone Has a Seat

138 pupils are going on a school trip. Each bus has seats for 40 pupils. (a) What is the smallest number of buses needed so that every pupil has a seat? (b) How many seats will be empty?

Pupils138 pupils
138 is about 140, and 140 ÷ 40 is between 3 and 4.
Estimate first. 138 is about 140, and 140 ÷ 40 is between 3 and 4. So test 3 buses and 4 buses.
step 1 of 5

Estimate the number of buses, then test the whole numbers on either side. The smaller number must be checked to see whether any pupils are left without a seat.

  1. Estimate first. 138 is about 140, and 140 ÷ 40 is between 3 and 4. So test 3 buses and 4 buses.
  2. 3 buses have 3 × 40 = 120 seats. That is fewer than 138, so 138 − 120 = 18 pupils would have no seat.
  3. 4 buses have 4 × 40 = 160 seats. That is enough for everyone, so round up to 4 buses.
  4. (a) The smallest number of buses needed is 4.
  5. (b) The number of empty seats is 160 − 138 = 22.

answer(a) 4 buses; (b) 22 seats

techniqueRounding to the Nearest Ten · Rounding to Estimate

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding down to 3 buses because 138 ÷ 40 = 3 remainder 18 is nearer to 3 than to 4. Then 18 pupils have no seat. When everyone must fit, round up.
  • Giving 18 as the number of empty seats. 18 is the number of pupils left over after 3 buses are full. The empty seats are on the fourth bus: 40 − 18 = 22.
05

A Digit Puzzle with a Rounded Number

strategyFind the Range First / Choose the Digits from the Left

Use each of the digits 4, 5, 8 and 0 once to make a 4-digit number. The number must be 5000 when it is rounded to the nearest thousand. (a) What is the smallest such number? (b) What is the largest such number?

458040005000600045005499
Every number from 4500 to 5499 rounds to 5000.
Find the numbers that round to 5000. The halfway numbers are 4500 and 5500, so the number must be from 4500 to 5499.
step 1 of 5

First find all the numbers that round to 5000. Then build the number one digit at a time from the left, keeping it inside that range.

  1. Find the numbers that round to 5000. The halfway numbers are 4500 and 5500, so the number must be from 4500 to 5499.
  2. For the smallest number, start with the thousands digit 4. The hundreds digit must then be 5 or more, so choose 5. Put the smaller of the last two digits first, 0 then 8.
  3. (a) The smallest such number is 4508.
  4. For the largest number, start with the thousands digit 5. The hundreds digit must then be 4 or less, so choose 4. Put the larger of the last two digits first, 8 then 0.
  5. (b) The largest such number is 5480.

answer(a) 4508; (b) 5480

techniqueRounding to the Nearest Hundred and Thousand · Ordering Numbers

examsPSLE · GCSE Higher

Common pitfalls

  • Giving 8540, the largest number the four digits can make. 8540 rounds to 9000, not to 5000.
  • Giving 4058 as the smallest number. 4058 is less than the halfway number 4500, so it rounds down to 4000.
06

The Halfway Number and the Number Just Before It

strategyCompare with the Halfway Number / A Halfway Number Rounds Up

Farm A has 2499 chickens and Farm B has 2500 chickens. Each number is rounded to the nearest thousand. (a) What is the rounded number for Farm A? (b) What is the rounded number for Farm B?

200025003000
Both numbers are between 2000 and 3000. The halfway number is 2500.
Both numbers are between 2000 and 3000. The halfway number is 2500.
step 1 of 5

Both numbers are between the same two thousands. Compare each number with the halfway number between those thousands.

  1. Both numbers are between 2000 and 3000. The halfway number is 2500.
  2. 2499 is less than the halfway number, so it is nearer to 2000. Round down.
  3. (a) For Farm A, 2499 rounds to 2000.
  4. 2500 is exactly halfway. It is 500 from 2000 and 500 from 3000. The rule is that a halfway number rounds up.
  5. (b) For Farm B, 2500 rounds to 3000.

answer(a) 2000; (b) 3000

techniqueRounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding 2500 down to 2000 because it is not nearer to 3000. It is not nearer to 2000 either, and the rule for a halfway number is to round up.
  • Rounding 2499 up because its last digits are 9 and 9. For the nearest thousand the hundreds digit decides, and the hundreds digit is 4.
07

Two Numbers That Round to the Same Hundred

strategyFind the Smallest and the Largest Possible Number / Choose the Ends of the Range

Two schools each say that they have about 700 pupils. Both numbers were rounded to the nearest hundred. (a) What is the greatest possible difference between the numbers of pupils in the two schools? (b) What is the greatest possible total number of pupils in the two schools?

600700800650749
Each school has from 650 to 749 pupils. 750 would round to 800.
Find the numbers that round to 700. The halfway number 650 rounds up to 700. The halfway number 750 rounds up to 800. So each school has from 650 to 749 pupils.
step 1 of 5

Find the smallest and the largest number that round to 700. The greatest difference uses both ends of the range, and the greatest total uses the largest number twice.

  1. Find the numbers that round to 700. The halfway number 650 rounds up to 700. The halfway number 750 rounds up to 800. So each school has from 650 to 749 pupils.
  2. The difference is greatest when one school has the smallest number and the other school has the largest number.
  3. (a) The greatest possible difference is 749 − 650 = 99.
  4. The total is greatest when both schools have the largest number, 749.
  5. (b) The greatest possible total is 749 + 749 = 1498.

answer(a) 99; (b) 1498

techniqueRounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Saying the difference is 0 because both numbers round to 700. The real numbers can be anywhere from 650 to 749, so they can be as much as 99 apart.
  • Using 750 as the largest number and giving a total of 1500. 750 rounds up to 800, so the largest number for each school is 749.
08

A Distance Table Rounded to the Nearest Hundred Kilometers

strategyRound Every Row / Go Back to the Real Numbers to Compare

Four towns are 238 km, 352 km, 449 km and 548 km from the city. They are Town A, Town B, Town C and Town D in that order. Each distance is rounded to the nearest hundred kilometers. (a) Two towns have the same rounded distance. What is that rounded distance? (b) How many kilometers farther from the city is one of these two towns than the other?

TownReal distance (km)Rounded (km)Town A238200Town B352400Town C449Town D548
The tens digit decides: 238 rounds down to 200 and 352 rounds up to 400.
Round each distance to the nearest hundred by looking at the tens digit. 238 rounds down to 200 and 352 rounds up to 400.
step 1 of 5

Round every distance in the table. Two towns with the same rounded distance can still be far apart, so compare them with the real distances.

  1. Round each distance to the nearest hundred by looking at the tens digit. 238 rounds down to 200 and 352 rounds up to 400.
  2. 449 rounds down to 400 and 548 rounds down to 500.
  3. (a) Town B and Town C both have a rounded distance of 400 km.
  4. Go back to the real distances to compare these two towns: 449 − 352 = 97.
  5. (b) Town C is 97 km farther from the city than Town B.

answer(a) 400 km, for Town B and Town C; (b) 97 km

techniqueRounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Saying Town B and Town C are the same distance from the city because both round to 400 km. The real distances are 352 km and 449 km, which are 97 km apart.
  • Rounding 449 up to 500 because of the 9 in the ones place. The tens digit decides, and it is 4, so 449 rounds down to 400.
09

A Product Estimated by Rounding Both Numbers

strategyRound Both Numbers to the Nearest Ten / Compare the Estimate with the Exact Product

A hall has 38 rows of chairs with 52 chairs in each row. (a) Estimate the number of chairs by rounding both numbers to the nearest ten. (b) How far is the estimate from the exact number of chairs?

38 × 5240 × 50exactestimate
38 rounds up to 40 and 52 rounds down to 50.
Round each number to the nearest ten. 38 rounds up to 40 and 52 rounds down to 50.
step 1 of 4

Round both numbers to the nearest ten and multiply the rounded numbers. Then multiply the real numbers and find the difference.

  1. Round each number to the nearest ten. 38 rounds up to 40 and 52 rounds down to 50.
  2. (a) The estimate is 40 × 50 = 2000 chairs.
  3. Find the exact number: 38 × 52 = 38 × 50 + 38 × 2 = 1900 + 76 = 1976.
  4. (b) The estimate is 2000 − 1976 = 24 chairs away from the exact number.

answer(a) 2000 chairs; (b) 24 chairs

techniqueRounding to the Nearest Ten · Rounding to Estimate

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding only one of the numbers, for example 38 × 50 = 1900. The question asks for both numbers to be rounded to the nearest ten.
  • Writing 40 × 50 = 200. 4 × 5 = 20, and there are two more zeros to put back, so the product is 2000.
10

A Number Placed Between Two Hundreds

strategyNumber Line / Find the Distance to Each End

Ben has 467 stickers. (a) How far is 467 from 400, and how far is it from 500? (b) Round 467 to the nearest hundred.

400450500467
467 is between 400 and 500. Each small mark is 10.
467 is between 400 and 500. Draw a number line from 400 to 500 and place 467 on it.
step 1 of 5

Draw a number line from 400 to 500 and place 467 on it. The nearer end of the line is the rounded number.

  1. 467 is between 400 and 500. Draw a number line from 400 to 500 and place 467 on it.
  2. Find the distance to each end: 467 − 400 = 67 and 500 − 467 = 33.
  3. (a) 467 is 67 from 400 and 33 from 500.
  4. 33 is less than 67, so 467 is nearer to 500.
  5. (b) To the nearest hundred, 467 is 500.

answer(a) 67 from 400 and 33 from 500; (b) 500

techniqueRounding to the Nearest Hundred and Thousand

examsPSLE · GCSE Higher

Common pitfalls

  • Rounding to 400 because 467 starts with a 4. 467 is past the halfway number 450, so it is nearer to 500.
  • Writing 500 − 467 = 43. Count up to check: 467 + 3 = 470 and 470 + 30 = 500, so the distance is 33.
Mr. Chalk Drill rounding