convert the following repeating decimal to a fraction simplest form
.40 ̅
To convert the repeating decimal .40 ̅ to a fraction, we can use the method of "place value" by subtracting the original number from the repeating number.
Let x = .40 ̅
Then, 10x = 4.40 ̅
Now, we can subtract the original number x from 10x:
10x - x = 4.40 ̅ - .40 ̅
9x = 4
To solve for x, we divide both sides by 9:
x = 4/9
Therefore, the fraction equivalent of the repeating decimal .40 ̅ is 4/9 in simplest form.
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To convert the repeating decimal .40 ̅ to a fraction, we can use the method of "place value" by subtracting the original number from the repeating number.
Let x = .40 ̅
Then, 100x = 40.40 ̅
Now, we can subtract the original number x from 100x:
100x - x = 40.40 ̅ - .40 ̅
99x = 40
To solve for x, we divide both sides by 99:
x = 40/99
Therefore, the fraction equivalent of the repeating decimal .40 ̅ is 40/99 in simplest form.
To convert the repeating decimal .40̅ to a fraction in simplest form, we can use the concept of infinite geometric series.
Let's represent .40̅ as x.
To remove the repeating part, we multiply x by 100 to get:
100x = 40.40̅
Next, we subtract the original equation, x, from both sides:
100x - x = 40.40̅ - .40̅
Simplifying, we have:
99x = 40
Now, we can solve for x by dividing both sides by 99:
x = 40/99
Therefore, .40̅ as a fraction in simplest form is 40/99.
To convert the repeating decimal .40 ̅ to a fraction in simplest form, you can follow these steps:
Step 1: Let's simplify the repeating decimal .40 ̅ by multiplying it by a power of 10 to eliminate the repeating part. Since there is only a single digit repeating (0), we can multiply by 10.
.40 ̅ * 10 = 4.40 ̅
Step 2: Now, we need to subtract the original decimal from the one obtained after multiplication. This will help eliminate the repeating part.
4.40 ̅ - .40 ̅ = 4
Step 3: Next, we need to determine the decimal place value of the repeating part. Since it's a single digit (0), it lies after the tenths place value.
Step 4: Now, we can create a fraction by putting the original decimal over a denominator with the same number of 9s as the number of digits in the repeating part. In this case, we have 1 digit, so we use 9 as the denominator.
The fraction is: .40 ̅ = 4/9