Write 121/200 as a decimal number.

The Correct Answer and Explanation is:

The correct answer is 0.605.

To write the fraction 121/200 as a decimal number, you need to perform the division that the fraction represents. The fraction bar signifies division, so 121/200 is equivalent to 121 divided by 200. There are a couple of effective methods to solve this.

Method 1: Using an Equivalent Fraction

This method involves converting the fraction into an equivalent one with a denominator that is a power of 10 (like 10, 100, 1000, etc.). This makes the conversion to a decimal very simple.

1. Look at the denominator, which is 200. Ask yourself what you can multiply 200 by to get a power of 10. Multiplying 200 by 5 gives you 1000, which is a power of 10.
2. To create an equivalent fraction, you must multiply both the numerator and the denominator by the same number. In this case, we multiply both by 5.
3. Multiply the numerator: 121 × 5 = 605.
4. Multiply the denominator: 200 × 5 = 1000.
5. The new, equivalent fraction is 605/1000.
6. This fraction is read as “six hundred five thousandths.” When you write this as a decimal, the last digit of the number 605 must be in the thousandths place (the third position after the decimal point). Therefore, 605/1000 is written as 0.605.

Method 2: Using Long Division

This method involves directly dividing the numerator by the denominator.

1. Set up the long division problem with 121 as the dividend and 200 as the divisor.
2. Since 121 is smaller than 200, you place a decimal point after 121 and add a zero, making it 121.0. Also place a decimal point in the answer space directly above.
3. Now, divide 1210 by 200. The number 200 goes into 1210 six times (6 × 200 = 1200). Write “6” after the decimal point in your answer.
4. Subtract 1200 from 1210, which leaves a remainder of 10.
5. Bring down another zero, making the new number 100.
6. Divide 100 by 200. Since 200 cannot go into 100, you write “0” in the next position in your answer.
7. Bring down one more zero, making the new number 1000.
8. Divide 1000 by 200. This goes in exactly five times (5 × 200 = 1000). Write “5” in the next position in your answer.
9. Subtract 1000 from 1000, which leaves a remainder of 0. The division is complete.

Both methods confirm that the fraction 121/200 is equal to the decimal number 0.605.