Question

Mia and Paul are looking at the same whole number.
Mia says that the number is to the nearest thousand it is 44000.
Paul says that the number is to the nearest ten it is 44000.
They are both correct.
Write down one possible value of the number.

Answer 1

Hint: Here from the question we know that both Mia and Paul are correct and both are looking at the same number and rounding off it to the nearest $ 1000's $ and $ 10's $ respectively. So for answering this question we will see for the range of values that will result in 44000 when they are rounded off to the nearest $ 1000's $ and to the nearest $ 10's $.

Complete step by step answer:
From the basic concept of rounding off to the nearest ten.
1) If a number we are rounding is followed by \[5,\text{ }6,\text{ }7,\text{ }8,\text{ }or\text{ }9\], round the number up, that means to the higher $ 10's $ . Example: $ 58 $ rounded to the nearest ten is $ 60 $ .
2) If the number we are rounding is followed by 0, 1, 2, 3, or 4, round the number down, that is to the lower $ 10's $. Example: $ 23 $ rounded to the nearest ten is $ 20 $ .

$\Rightarrow$ From the basic concept rounding off to the nearest $ 1000's $,
1) If a number we are rounding is followed by \[500,\text{ }600,\text{ }700,\text{ }800,\text{ }or\text{ }900\], round the number up, that means to the higher $ 1000's $ . Example: $ 7800 $ rounded to the nearest $ 1000's $ is $ 8000 $ .
2) If the number we are rounding is followed by \[0,\text{ }100,\text{ }200,\text{ }300,\text{ }or\text{ }400\], round the number down, that is to the lower $ 1000's $ . Example: $ 3400 $ rounded to the nearest $ 1000's $ is $ 3000 $ .

Here in this question, it is given that Mia and Paul are looking at the same number.
$\Rightarrow$ According to the point of view of Mia when the number is rounded to the nearest $ 1000's $ it gives $ 44000 $. This implies that the number is in between \[44000\text{ }to\text{ }44499\].
$\Rightarrow$ According to the point of view of Paul when the number is rounded to the nearest $ 10's $ , it gives $ 44000 $ . This implies that the number is in between \[44000\text{ }to\text{ }44005\].
$\Rightarrow$ According to the question both are correct, the possible value of the number will be in between \[44000\text{ and }44005\].

Note:
While trying to answer this question we should be careful with the concept of rounding off if we unfortunately rounded off the numbers incorrectly and answered the question as range between\[44000\text{ }to\text{ }44009\text{ }or\text{ }44000\text{ }to\text{ }44999\]. It will be a complete wrong answer.