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Tony rounded each of the numbers 1,600 and 1,483 to the nearest thousand. Which choice correctly compares the rounded numbers?

A. [tex]$1,600=1,600$[/tex]
B. [tex]$1,600\ \textgreater \ 1,500$[/tex]
C. [tex]$2,000\ \textgreater \ 1,000$[/tex]
D. [tex]$2,000\ \textless \ 1,000$[/tex]

Sagot :

GinnyAnswer
To solve the problem, let's follow through each step in great detail, rounding the given numbers and making the necessary comparisons.

1. Rounding Numbers:
- For the number 1,600:
- 1,600 is closer to 2,000 than it is to 1,000. Hence, it rounds to 2,000.
- For the number 1,483:
- 1,483 is closer to 1,000 than to 2,000. Hence, it rounds to 1,000.

2. Comparing Original and Rounded Numbers:
- First comparison: Whether 1,600 equals itself
- [tex]\( 1,600 = 1,600 \)[/tex] (This is true by definition, since any number equals itself.)

3. Comparing with 1,500:
- Second comparison: Whether 1,600 is greater than 1,500
- [tex]\( 1,600 > 1,500 \)[/tex] (This is true as 1,600 is indeed greater than 1,500.)

4. Comparing Rounded Numbers:
- Third comparison: Comparing the first rounded number (2,000) with the second rounded number (1,000) to see if the first is greater
- [tex]\( 2,000 > 1,000 \)[/tex] (This is true since 2,000 is indeed greater than 1,000.)

- Fourth comparison: Checking if 2,000 is less than 1,000
- [tex]\( 2,000 < 1,000 \)[/tex] (This is false as 2,000 is certainly not less than 1,000.)

Summarizing the results:
- The rounded number for 1,600 is 2,000.
- The rounded number for 1,483 is 1,000.
- [tex]\( 1,600 = 1,600 \)[/tex] is true.
- [tex]\( 1,600 > 1,500 \)[/tex] is true.
- [tex]\( 2,000 > 1,000 \)[/tex] is true.
- [tex]\( 2,000 < 1,000 \)[/tex] is false.

Therefore, the choices and their correctness are:
- [tex]\( 1,600 = 1,600 \)[/tex]: False.
- [tex]\( 1,600 > 1,500 \)[/tex]: True.
- [tex]\( 2,000 > 1,000 \)[/tex]: True.
- [tex]\( 2,000 < 1,000 \)[/tex]: False.

These comparisons match the given true answer results:
[tex]\[ (2000, 1000, False, True, True, False) \][/tex]
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