how do i change 0.26(2/3) to a fraction
0.26(2/3) = 0.52/3
= 52/300 = 13/75
Who did you came up with that answer?
To change 0.26(2/3) to a fraction, follow these steps:
Step 1: Write the fractional part as a decimal. In this case, 2/3 is equal to 0.6666...
Step 2: Determine the number of decimal places in the original decimal. Since there are 2 decimal places in 0.26, we need to multiply the fractional part by 100 (since there are two decimal places) to move the decimal point to the right.
0.6666... × 100 = 66.666...
Step 3: Write the resulting number as a fraction over the appropriate power of 10. Here, the number has two decimal places, so we put it over 100.
66.666... / 100
Step 4: Simplify the fraction if possible. In this case, we can simplify by dividing both the numerator and the denominator by 2.
66.666... / 100 = 33.333... / 50
Step 5: Write the simplified fraction as a mixed number. In this case, 33.333... / 50 can be written as 33 and one-third over 50.
Therefore, 0.26(2/3) can be written as the fraction 33 1/3 over 50.
To change the decimal 0.26(2/3) to a fraction, we need to understand that the digits after the decimal point will repeat indefinitely. This is indicated by the parentheses in the number.
Step 1: Let's represent the repeating decimal as x. So, x = 0.26(2/3).
Step 2: Multiply both sides of the equation by 100 to eliminate the decimal. This gives us 100x = 26.66(2/3).
Step 3: Since there are two digits repeating after the decimal point, we need to subtract a smaller equation where the repeating decimal is removed. So, 10x = 2.66(2/3).
Step 4: Subtract the equation obtained in step 3 from the equation in step 2: (100x - 10x) = 26.66(2/3) - 2.66(2/3).
Step 5: Simplify the equation: 90x = 24.
Step 6: Divide both sides of the equation by 90 to isolate x: x = 24/90.
Step 7: Reduce the fraction by dividing both the numerator and denominator by their greatest common divisor. In this case, the greatest common divisor is 6, so the fraction becomes x = 4/15.
Therefore, 0.26(2/3) is equivalent to the fraction 4/15.