Question

What is the number rounded to the nearest thousand? `12,543`

Answer 1

`12543` rounded to the nearest thousands is `13000`.

Explanation:

Breakdown of the number `12543`.

`"1 ten thousands"`

`"2 one thousands"`

`"5 hundreds"`

`"4 tens"`

`"3 ones"`

When rounding a number, you look at the digit directly to its right. If that digit is less than `5`, the digit to be rounded remains the same. If the digit directly to the right is `5` or greater, the digit to be rounded is increased by `1`.

In the number `12color(red)(5)43`, the digit in the hundreds place is `5`, so the digit in the thousands place will be rounded up to `3`.

`12543` rounded to the nearest thousands is `13000`.

Answer 2

13,000

Explanation:

We have a 5-digit number. The thousands place is the 4th digit to the left of the decimal:

`1ul2,color(red)(5)color(blue)(4)color(orange)(3)`

So we need to have our last digit that is not a zero be at this position (the underlined digit).

A number rounded to the nearest thousand must be a multiple of `1,000`

The convention for rounding is:
- if a digit is less than `5`, change the digit to a `0` and do not modify the digit immediately to its left
- if a digit is equal to or greater than `5`, change the digit to a `0` and add `1` to the digit immediately to its left

So we apply this as follows:

The first digit all the way on the right is `color(orange)(3)`. Since it is less than `5`, we make it a `color(orange)(0)` and do not change the `color(blue)(4)` that is to its left.

Now we have: `1ul2,color(red)(5)color(blue)(4)color(orange)(0)`

The first digit all the way on the right (that is not `0`) is `color(blue)(4)`. Since it is less than `5`, we make it a `color(blue)(0)` and do not change the `color(red)(5)` that is to its left.

Now we have: `1ul2,color(red)(5)color(blue)(0)color(orange)(0)`

The first digit all the way on the right (that is not `0`) is `color(red)(5)`. Since it is equal to or greater than `5`, we make it a `color(red)(0)` and add 1 to the `ul2` that is to its left.

Now we have: `1ul3,color(red)(0)color(blue)(0)color(orange)(0)`

Since we have reached the thousands place, we are finished. So the rounded number is:

`color(green)(13,000)`

Answer 3

13000

Explanation:

To round a positive integer to a particular power of ten (`10^x`), take half of the power of ten (`10^x/2`), add it to the positive integer, and force the last (least significant) `x` digits of the new sum to zero (`0`).

For example:

Rounding to the nearest `1color(blue)(000)` (`= 10*10*10 = 10^color(blue)(3)`)

`1000/2 = 500`

`12543 + 500 = 13043`

Force the last `3` digits to `color(blue)(0)`

`13color(blue)(000)`