Describe two methods to convert 9/20 to a decimal.
The Correct Answer and Explanation is:
To convert the fraction 920\frac{9}{20}209 into a decimal, two common methods can be employed: long division and multiplying by the reciprocal.
1. Long Division Method
The long division method is the most straightforward approach. Here’s the step-by-step process:
- Step 1: Divide 9 by 20.
- Step 2: Set up the division as 9÷209 \div 209÷20. Since 20 does not go into 9 directly, we add a decimal point and a zero to the dividend (making it 90).
- Step 3: Now divide 90 by 20. 20 goes into 90 four times (since 20×4=8020 \times 4 = 8020×4=80).
- Step 4: Subtract 808080 from 909090, which gives a remainder of 10.
- Step 5: Bring down another zero, making it 100. Divide 100 by 20, which goes exactly 5 times (since 20×5=10020 \times 5 = 10020×5=100).
- Step 6: The remainder is now zero, so the division stops here.
The result of the division is 0.450.450.45. Therefore, 920\frac{9}{20}209 as a decimal is 0.45.
2. Multiplying by the Reciprocal Method
Another way to convert 920\frac{9}{20}209 to a decimal is by multiplying by the reciprocal of the denominator. The reciprocal of 20 is 120\frac{1}{20}201, so we can use this method as follows:
- Step 1: Write the fraction as 9×1209 \times \frac{1}{20}9×201.
- Step 2: Convert 120\frac{1}{20}201 to a decimal, which is 0.050.050.05.
- Step 3: Multiply 9×0.059 \times 0.059×0.05. This gives 0.450.450.45.
Thus, multiplying by the reciprocal also gives 0.450.450.45 as the decimal equivalent of 920\frac{9}{20}209.
Conclusion
Both methods yield the same result, confirming that 920\frac{9}{20}209 as a decimal is 0.45.
