Sure! Let's address each part of the question step by step:
### Part 1: Rounding [tex]$476,305,821$[/tex] to the nearest million
To round [tex]$476,305,821$[/tex] to the nearest million, we need to examine the digit in the hundred thousands place:
- The millions digit in [tex]$476,305,821$[/tex] is [tex]$6$[/tex] (the [tex]$6$[/tex] in the millions place).
- The digit in the hundred thousands place (the [tex]$3$[/tex] in [tex]$476,305,821$[/tex]) is less than [tex]$5$[/tex].
Since the hundred thousands digit is less than [tex]$5$[/tex], the millions place remains the same, and all digits to the right of it turn into zeros. Thus, [tex]$476,305,821$[/tex] rounded to the nearest million is:
[tex]\[ 476,000,000 \][/tex]
### Part 2: Finding "two and one half" of [tex]$4 \frac{2}{3}$[/tex]
To find "two and one half" of [tex]$4 \frac{2}{3}$[/tex], we start by converting the mixed number into an improper fraction:
1. Convert the whole number part and the fraction separately:
- The whole number part is [tex]$4$[/tex].
- The fractional part is [tex]$\frac{2}{3}$[/tex].
2. Combine these by converting the whole number part into a fraction with the same denominator ([tex]$3$[/tex]):
[tex]\[ 4 = \frac{12}{3} \][/tex]
3. Add the fractional part to this:
[tex]\[ 4 \frac{2}{3} = \frac{12}{3} + \frac{2}{3} \][/tex]
[tex]\[ 4 \frac{2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \][/tex]
Now, we need to find "two and one half" (which is [tex]$2.5$[/tex]) of [tex]$\frac{14}{3}$[/tex]:
1. Multiply [tex]$2.5$[/tex] by [tex]$\frac{14}{3}$[/tex]:
[tex]\[ 2.5 \times \frac{14}{3} \][/tex]
2. Convert [tex]$2.5$[/tex] to a fraction:
[tex]\[ 2.5 = \frac{5}{2} \][/tex]
3. Multiply the fractions:
[tex]\[ \frac{5}{2} \times \frac{14}{3} = \frac{5 \times 14}{2 \times 3} = \frac{70}{6} \][/tex]
4. Simplify the fraction by dividing both the numerator and the denominator by [tex]$2$[/tex]:
[tex]\[ \frac{70}{6} = \frac{35}{3} \][/tex]
5. Convert back to a decimal to get the answer:
[tex]\[ \frac{35}{3} = 11.666666666666668 \][/tex]
Thus, the complete answer is:
1. [tex]$476,305,821$[/tex] rounded to the nearest million is [tex]$476,000,000$[/tex].
2. "Two and one half" of [tex]$4 \frac{2}{3}$[/tex] is [tex]$11.666666666666668$[/tex].
