What strategies do you use when converting a fraction to a decimal or a decimal to a fraction. (Essay answer) Help Thanks
When converting a fraction to a decimal, or vice versa, there are distinct strategies that can guide you through the process. Let's delve into each conversion method step by step.
1. Converting a fraction to a decimal:
a. Divide the numerator (top number) of the fraction by the denominator (bottom number). For example, if you have the fraction 3/4, you would divide 3 ÷ 4. In this case, the quotient is 0.75.
b. If the division results in a terminating decimal (a decimal that ends after a certain number of decimal places), you are finished. The fraction 3/4, for instance, converts directly to the decimal 0.75.
c. However, if the division results in a repeating decimal (a decimal that repeats a pattern of numbers indefinitely), you need to follow an additional step. Consider the fraction 2/3. Divide 2 by 3, which yields 0.666..., indicating an infinite repetition of the digit 6. To express this repeating decimal in a simplified form, you can use a bar notation. In this case, the fraction 2/3 is equivalent to 0.6̅ (with the bar placed above the 6 to denote the repeated pattern).
2. Converting a decimal to a fraction:
a. Identify the place value of the last digit in the decimal. This will determine the denominator of the resulting fraction. For instance, if you have the decimal 0.32, the last digit resides in the hundredths place, so the denominator will be 100.
b. Write the decimal as the numerator of the fraction. In our example, the decimal 0.32 becomes 32/100.
c. Simplify the fraction, if possible, by dividing the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor of 32 and 100 is 4. Dividing both the numerator and denominator by 4 results in the simplified fraction 8/25.
It's worth noting that converting between fractions and decimals can be approached using other methods as well. These steps serve as a general guide to get you started. By mastering these strategies, you will be able to smoothly and accurately convert between fractions and decimals.
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