To convert 0.833 to a fraction, write the number without the decimal point over 1000, since there are three digits after the decimal. This gives 833/1000. To simplify, check for common factors between the numerator and denominator. Since 833 (7² * 17) and 1000 (2³ * 5³) share no common factors other than 1, the fraction 833/1000 is already in...
The repeating decimal 0.833... is equivalent to the simplified fraction 5/6. This is determined by setting x equal to the decimal. Manipulate by multiplying by powers of ten, subtract equations to eliminate the repeating part, giving 90x = 75. Simplify 75/90 to 5/6.
The repeating decimal 0.333... is represented by the simplified fraction 1/3. This conversion is straightforward: let x = 0.333..., then 10x = 3.333.... Subtracting x from 10x gives 9x = 3. Therefore, x = 3/9, which simplifies to 1/3.
The repeating decimal 0.666... is equal to the simplified fraction 2/3. To find this, set x = 0.666.... Then 10x = 6.666.... Subtracting x from 10x yields 9x = 6. Solving for x gives 6/9, which reduces to 2/3 in its simplest form.
Yes, 0.166... (with the 6 repeating) is equivalent to the fraction 1/6. This is a common mixed repeating decimal. The conversion involves setting x equal to the decimal, then solving the equation 90x = 15. This yields x = 15/90, which easily simplifies to 1/6.
The repeating decimal 0.111... (where the '1' repeats) converts to the simplified fraction 1/9. This is a pure repeating decimal. Let x = 0.111.... Then 10x = 1.111.... Subtracting x from 10x results in 9x = 1. Solving for x gives the fraction 1/9.
The repeating decimal 0.444... is equivalent to the common fraction 4/9. This pure repeating decimal is converted by letting x = 0.444.... Then 10x = 4.444.... Subtracting x from 10x yields 9x = 4. Solving for x directly gives 4/9, already simplified.
The decimal 0.83, which is not a repeating decimal, converts to the simplified fraction 83/100. This conversion simply involves placing the digits after the decimal point over the appropriate power of ten. As there are two decimal places, it becomes 83/100, which is already in its simplest form.
The decimal 0.16, which is not a repeating decimal, converts to the simplified fraction 4/25. To convert, write it as 16/100. Then, simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4. This process leads directly to the simplified form of 4/25.
To convert, assign the repeating decimal to a variable 'x'. Multiply 'x' by powers of ten to create equations where the repeating digits align. Subtract these equations to eliminate the repeating part. Solve the resulting algebraic expression for 'x', then simplify the obtained fraction.
The repeating decimal 0.222... is equivalent to the simplified fraction 2/9. This pure repeating decimal is converted by setting x = 0.222.... Then 10x = 2.222.... Subtracting x from 10x yields 9x = 2. Solving for x gives 2/9, which is already in its simplest form.