Rounding

Worked example

1. 1

   $268$ — Nearest 10 means the answer is a whole number of tens. The digit just right of the tens is the units digit, 8, so it decides.

2. 2

   $8\ge 5$ — 8 is 5 or more, so 268 is past halfway (265). Round up.

3. 3

   $26\text{ tens}\to 27\text{ tens}$ — Rounding up adds 1 to the tens digit: 6 tens becomes 7 tens.

4. 4

   $270$ — Put 0 in the units place. 270 is a whole number of tens and is still about the same size as 268.

Worked example

1. 1

   $58746$ — Nearest thousand means the answer is a whole number of thousands. There are 58 thousands.

2. 2

   $58746$ — The digit just right of the thousands is the hundreds digit, 7. Only this digit decides.

3. 3

   $7\ge 5$ — 7 is 5 or more, so 58 746 is past halfway (58 500). Round up.

4. 4

   $58\text{ thousands}\to 59\text{ thousands}$ — Rounding up adds 1 to the thousands.

5. 5

   $59000$ — Put 0 in the hundreds, tens and units, so the answer keeps its size.

Worked example

1. 1

   $7349$ — Nearest hundred means the answer is a whole number of hundreds. The hundreds digit is 3, so there are 73 hundreds.

2. 2

   $7349$ — The digit just right of the hundreds is the tens digit, 4. It decides. The 9 after it does not count.

3. 3

   $4<5$ — 4 is less than 5, so 7349 is below halfway (7350). Round down.

4. 4

   $7300$ — Rounding down keeps the 3 as it is. Put 0 in the tens and units.

Worked example

1. 1

   $4725$ — Nearest ten: there are 472 tens. The digit just right of the tens is the units digit, 5, so it decides.

2. 2

   $5\ge 5$ — 4725 is exactly halfway between 4720 and 4730. Halfway always rounds up.

3. 3

   $472\text{ tens}\to 473\text{ tens}$ — Rounding up adds 1 to the tens.

4. 4

   $4730$ — Put 0 in the units place, so the answer is a whole number of tens.

Worked example

1. 1

   $63.8$ — Nearest 10: the units digit, 3, is just right of the tens, so it decides. The 8 after the point does not count.

2. 2

   $3<5$ — 3 is less than 5, so round down: keep the 6 tens.

3. 3

   $60$ — Put 0 in the units and drop everything after the point. A whole ten has no decimal part.

Worked example

1. 1

   $63.8$ — Nearest whole number: the first digit after the point, 8, decides.

2. 2

   $8\ge 5$ — 8 is 5 or more, so round up: 63 becomes 64.

3. 3

   $64$ — Drop the digits after the point. A whole number has nothing after it.

Worked example

1. 1

   $30$ — A whole number rounds to 30 to the nearest ten. It must be nearer 30 than 20 or 40.

2. 2

   $25$ — Halfway down to 20 is 25. Halfway rounds up, so 25 rounds to 30. It is in.

3. 3

   $35$ — Halfway up to 40 is 35. It rounds up to 40, so 35 is out.

4. 4

   $25,26,\dots ,34$ — So the number is any whole number from 25 to 34.

Worked example

1. 1

   $24,32,40$ — List the multiples of 8 near 30.

2. 2

   $24<25$ — 24 is below 25, so it rounds to 20. Out.

3. 3

   $40>34$ — 40 is past 34. Out.

4. 4

   $32$ — 32 is between 25 and 34, so the number is 32.