To divide 210.21 by 36, we follow these steps:
1. Setup the Division:
- 210.21 is our dividend.
- 36 is our divisor.
2. Perform Division Step-by-Step:
- First Digit: Determine how many times 36 fits into the leading part of 210.21.
- 36 fits into 210 five times (because [tex]\( 36 \times 5 = 180 \)[/tex]).
- So, we place 5 in the quotient and subtract [tex]\( 36 \times 5 = 180 \)[/tex] from 210:
[tex]\[
210 - 180 = 30
\][/tex]
- Bring Down the Next Digit: Then, we bring down the next digit from 210.21. The 0 from 210 has already been handled, and we bring down the 2 from after the decimal point, giving us 302.
- Second Digit: Determine how many times 36 fits into 302:
- 36 fits into 302 eight times (because [tex]\( 36 \times 8 = 288 \)[/tex]).
- So, we place 8 in the quotient and subtract [tex]\( 36 \times 8 = 288 \)[/tex] from 302:
[tex]\[
302 - 288 = 14
\][/tex]
- Bring Down the Next Digit: Next, we bring down the next digit, which is 1 from 210.21 to give us 141.
- Third Digit: Determine how many times 36 fits into 141:
- 36 fits into 141 three times (because [tex]\( 36 \times 3 = 108 \)[/tex]).
- So, we place 3 in the quotient and subtract [tex]\( 36 \times 3 = 108 \)[/tex] from 141:
[tex]\[
141 - 108 = 33
\][/tex]
- Bring Down the Final Digit: Finally, since 33 is still less than 36, we bring down the additional 1 from the process, making it 330.
- Fourth Digit: Determine how many times 36 fits into 330:
- 36 fits into 330 nine times (because [tex]\( 36 \times 9 = 324 \)[/tex]).
- So, we place 9 in the quotient and subtract [tex]\( 36 \times 9 = 324 \)[/tex] from 330:
[tex]\[
330 - 324 = 6
\][/tex]
3. Result: The full division results in 5.839 (continuing the decimal division if needed). Therefore, the final quotient is
[tex]\[
5.839166666666667
\][/tex]
So, [tex]\( \frac{210.21}{36} = 5.839166666666667 \)[/tex].
