How do u do the problem 33.8 divided by 32.5?
The correct answer and explanation is:
Sure! Let’s solve 33.8 ÷ 32.5 step-by-step, and I’ll explain the process clearly.
Step 1: Understand the problem
You want to divide 33.8 by 32.5. This means you want to find how many times 32.5 fits into 33.8.
Step 2: Make the division easier by eliminating decimals
Dividing decimals directly can be tricky, so a common method is to remove the decimals by multiplying both numbers by the same power of 10.
- 33.8 has one decimal place.
- 32.5 has one decimal place.
Multiply both by 10 to get rid of the decimals: 33.8×10=33833.8 \times 10 = 338 32.5×10=32532.5 \times 10 = 325
Now the problem becomes: 338÷325338 \div 325
Step 3: Divide the whole numbers
Now divide 338 by 325.
- 325 fits into 338 once (because 2 times 325 = 650 which is too big).
- So, the quotient starts with 1.
Calculate the remainder: 338−325=13338 – 325 = 13
Step 4: Express remainder as decimal
To get a more precise answer, add decimal places.
- Add a decimal point and zeros to 338 (making it 338.0, 338.00, etc.) to continue dividing.
Bring down a zero (making the remainder 130):
- How many times does 325 fit into 130? 0 times.
Put 0 after the decimal: 1.0
Bring down another zero (making remainder 1300):
- 325 fits into 1300 about 4 times (325 × 4 = 1300 exactly).
So, next digit is 4.
Step 5: Final answer
The quotient is approximately 1.04.
Step 6: Verification
Multiply 32.5 × 1.04: 32.5×1.04=33.832.5 \times 1.04 = 33.8
So, the answer checks out.
Final answer:
33.8÷32.5=1.0433.8 \div 32.5 = 1.04
Explanation Summary (300 words)
Dividing decimals like 33.8 by 32.5 can be simplified by eliminating the decimals first. This is done by multiplying both numbers by the same power of 10 so that both become whole numbers. Since both numbers have one decimal place, multiplying by 10 moves the decimal point to the right by one digit, converting 33.8 to 338 and 32.5 to 325. Now the problem is a simple division of two whole numbers: 338 divided by 325.
When you divide 338 by 325, 325 fits into 338 once, leaving a remainder of 13. To find a more accurate answer including decimal points, you add decimal places by bringing down zeros, turning the remainder into 130, then 1300, and so forth. This process is similar to long division with whole numbers but continues beyond the decimal point.
Since 325 goes into 1300 exactly 4 times, the decimal expansion begins with 1.04. Multiplying 32.5 by 1.04 gives you back 33.8, confirming the division is correct.
In general, when dividing decimals, always try to convert the division into whole numbers first by multiplying numerator and denominator by powers of 10. This technique simplifies calculations and makes it easier to apply long division methods. The result is a decimal quotient that tells you how many times the divisor fits into the dividend. This approach can be used for any division involving decimals, making the process both efficient and reliable.