To round the number [tex]\(4,096,154\)[/tex] to the nearest 2,000, follow these steps:
1. Identify the value we're rounding to:
We're rounding to the nearest 2,000. This means we'll consider 2,000 as our rounding interval.
2. Find the number of intervals of 2,000 within [tex]\(4,096,154\)[/tex]:
We need to determine how many full intervals of 2,000 fit into [tex]\(4,096,154\)[/tex]. This can be thought of as dividing [tex]\(4,096,154\)[/tex] by 2,000.
3. Determine the nearest whole interval:
Determine the whole number of intervals and identify whether to round up or down by checking which multiple of 2,000 is closest to [tex]\(4,096,154\)[/tex].
4. Calculate the rounded value:
Multiply the nearest whole interval by 2,000 to get the rounded value.
Let's illustrate:
- [tex]\(4,096,154\)[/tex] divided by [tex]\(2,000\)[/tex] gives approximately [tex]\(2048.077\)[/tex].
- Since the decimal part [tex]\(0.077\)[/tex] is less than 0.5, we round down to [tex]\(2048\)[/tex].
Finally, multiply [tex]\(2048\)[/tex] by [tex]\(2,000\)[/tex]:
[tex]\[2048 \times 2000 = 4,096,000\][/tex]
Therefore, rounding [tex]\(4,096,154\)[/tex] to the nearest 2,000 gives us [tex]\(4,096,000\)[/tex].
The correct answer is C. [tex]\($4,096,000$\)[/tex].
