Divide. Write your answer as a decimal. 0.459 divided by 0.17
The Correct Answer and Explanation is:
Correct Answer: 0.459÷0.17=2.70.459 \div 0.17 = 2.70.459÷0.17=2.7
Explanation:
To divide 0.459 by 0.17 and write the answer as a decimal, we follow a step-by-step approach. This involves eliminating the decimal places in the divisor (0.17), performing the division, and interpreting the result.
Step 1: Remove the decimals from the divisor
The divisor is 0.17, which has two decimal places. To make the division easier, multiply both the dividend and the divisor by 100. This changes the problem to: 0.459×1000.17×100=45.917\frac{0.459 \times 100}{0.17 \times 100} = \frac{45.9}{17}0.17×1000.459×100=1745.9
Now the problem becomes: divide 45.9 by 17.
Step 2: Perform long division
We divide 45.9 by 17:
- 17 goes into 45 two times (17 × 2 = 34)
- Subtract 34 from 45 gives 11
- Bring down the 9 (from the decimal part), making it 119
- 17 goes into 119 seven times (17 × 7 = 119)
So, 45.9÷17=2.745.9 \div 17 = 2.745.9÷17=2.7
Step 3: Interpret the result
The result of the division is 2.7, which is a terminating decimal.
Why This Works:
Decimal division can be tricky due to the presence of decimal points, but the key idea is to make the divisor a whole number. This simplifies the division process. Multiplying both the numerator and denominator by the same factor (in this case, 100) does not change the value of the expression, because you’re essentially multiplying by 1 in a disguised form.
Thus, the final answer is: 2.7\boxed{2.7}2.7
This decimal represents the number of times 0.17 fits into 0.459.
