To solve this problem, we'll identify the value of the underlined 3 and then determine which of the other 3s in the number has a value that is equal to [tex]$\frac{1}{10}$[/tex] of this value.
1. Identify the value of the underlined 3:
- The number given is [tex]\(6,033,378\)[/tex].
- The underlined 3 is in the ten-thousands place.
- The value of a digit in a positional number system is determined by its place value. So, in this case, the underlined 3, being in the ten-thousands place, has a value of [tex]\(30,000\)[/tex].
2. Calculate [tex]$\frac{1}{10}$[/tex] of the value of the underlined 3:
- The value of the underlined 3 is [tex]\(30,000\)[/tex].
- To find [tex]$\frac{1}{10}$[/tex] of [tex]\(30,000\)[/tex], we divide [tex]\(30,000\)[/tex] by [tex]\(10\)[/tex]:
[tex]\[
\frac{30,000}{10} = 3,000
\][/tex]
3. Identify the value of each 3 in the number [tex]\(6,033,378\)[/tex]:
- The first 3 from the left (after the underlined 3) is in the thousands place. Its value is [tex]\(3 \times 1,000 = 3,000\)[/tex].
- The second 3 from the left (the underlined 3) we know is [tex]\(30,000\)[/tex].
- The third 3 (in the hundreds place) is [tex]\(3 \times 100 = 300\)[/tex].
4. Determine which 3 has the value equal to [tex]$\frac{1}{10}$[/tex] of the underlined 3:
- We found that [tex]$\frac{1}{10}$[/tex] of the value of the underlined 3 (which is [tex]\(30,000\)[/tex]) is [tex]\(3,000\)[/tex].
- The 3 in the thousands place has a value of [tex]\(3,000\)[/tex].
Therefore, the 3 in the thousands place is the one that has a value equal to [tex]$\frac{1}{10}$[/tex] of the value of the underlined 3. Thus, you should circle the 3 in the thousands place:
[tex]\[
6,03\underline{3},378
\][/tex]
