Convert 0.27¯¯¯¯¯
to a rational number in simplest form.(1 point)
Responses
127
Start Fraction 1 over 27 end fraction
311
Start Fraction 3 over 11 end fraction
2799
Start Fraction 27 over 99 end fraction
27100
Start Fraction 27 over 100 end fraction
To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?(1 point)
Responses
1,000
1,000
100
100
999
999
10
1,000
If a repeating decimal has a repeating cycle of three digits, it will convert to a rational number with what denominator? (1 point)
Responses
100
100
1,000
1,000
999
999
99
99
To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we will use the concept of repeating decimals.
Step 1: Let x = 0.27¯¯¯¯¯.
Step 2: Multiply both sides of the equation by 100 to remove the repeating decimal:
100x = 27.¯¯¯¯¯.
Step 3: Subtract the original equation from the equation obtained in step 2:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯.
Simplifying both sides of the equation:
99x = 27.
Step 4: Divide both sides of the equation by 99 to isolate x:
99x/99 = 27/99.
Simplifying both sides of the equation:
x = 27/99.
Therefore, 0.27¯¯¯¯¯ can be expressed as the rational number Start Fraction 27 over 99 end fraction in simplest form.
To convert a repeating decimal to a rational number in simplest form, we need to use the concept of fractions.
The repeating decimal 0.27¯¯¯¯¯ can be represented as a fraction by following these steps:
1. Let x = 0.27¯¯¯¯¯
2. Multiply both sides of the equation by 100 (because there are two decimal places in 0.27¯¯¯¯¯) to get 100x = 27.¯¯¯¯¯.
3. Now, we can subtract the original equation from the multiplied equation to eliminate the repeating decimal: 100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯.
This simplifies to 99x = 27.
4. Divide both sides of the equation by 99 to solve for x: x = 27/99.
5. Simplify the fraction 27/99 to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 9:
27 ÷ 9 / 99 ÷ 9 = 3/11.
Therefore, the rational number in simplest form for 0.27¯¯¯¯¯ is Start Fraction 3 over 11 end fraction.