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

3 Answers
Mar 18, 2018

#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#.

Mar 18, 2018

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)#

Mar 18, 2018

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)#