show me how to convert a decimal into a fraction in simplest form
drop the decimal place and use that resulting number as your numerator.
The denominator is a power of 10, were the exponent is the number of decimal places you had in your original number.
i.e. a 1 followed by as many zeros as you had decimal places
e.g. 0.123 = 123/1000
reduce the fraction to its lowest terms if possible
Alternatively:
N = .123
1000N = 123
N = 123/1000
Sure! To convert a decimal into a fraction in simplest form, you need to follow these steps:
Step 1: Determine the denominator
The denominator of the fraction will depend on the number of decimal places present in the decimal. Keep in mind that the decimal places determine the powers of 10.
For example, if there are no decimal places, the denominator will be 1 (i.e., 10^0 = 1). If there is one decimal place, the denominator will be 10 (i.e., 10^1 = 10). If there are two decimal places, the denominator will be 100 (i.e., 10^2 = 100), and so on.
Step 2: Rewrite the decimal as a fraction
Now that you have the denominator, you can rewrite the given decimal as a fraction. The numerator of the fraction will be the decimal after removing the decimal point.
For example, if the decimal is 0.75, remove the decimal point and use 75 as the numerator. If the decimal is 3.14, use 314 as the numerator.
Step 3: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator. Divide both the numerator and the denominator by their GCD. The resulting fraction, when written in its simplest form, will be your answer.
For example, let's convert the decimal 0.75 into a fraction in simplest form:
Step 1: The decimal has two decimal places, so the denominator will be 100.
Step 2: The numerator is 75.
Step 3: To simplify the fraction, find the GCD of 75 and 100. The GCD is 25.
Now, divide both the numerator and denominator by 25:
75 ÷ 25 = 3, and 100 ÷ 25 = 4.
Therefore, the simplest form of the fraction is 3/4.
So, 0.75 is equivalent to 3/4 in its simplest form.