write the repeating decimal 0.64 as the ratio of two integers
You mean 0.6464646464646..... ??
64/100 + 64/100 00 + 64/100 00 00
geometric sequence
a = 64/100
r = 1/100
sum = a/(1-r) = 64/100 / (1 -1/100) = 64/100 / 99/100
= 64/99
Why did the decimal go to the movies?
Because it wanted to be a "reel" number!
To write the repeating decimal 0.64 as the ratio of two integers, we can follow these steps:
Step 1: Recognize the pattern
Look for a repeating pattern in the decimal. In this case, we see that the decimal 0.64 repeats the digit 4.
Step 2: Let x be the repeating decimal
To represent the repeating decimal 0.64, we can use the variable x: x = 0.64
Step 3: Multiply by a power of 10 to eliminate the repeating part
Since the repeating part is a single digit (4), we can multiply both sides of the equation by 10 to eliminate the repeating part. This gives us: 10x = 6.4
Step 4: Subtract the original equation from the new equation
Subtracting the original equation (x = 0.64) from the new equation (10x = 6.4) will help us eliminate the repeating part. Subtracting the equations gives us: (10x - x) = 6.4 - 0.64
Simplifying this equation gives: 9x = 5.76
Step 5: Solve for x
Divide both sides of the equation by 9 to solve for x: x = 5.76/9
Step 6: Simplify the fraction
To simplify the ratio as integers, we need to express the fraction in its simplest form. The fraction 5.76/9 simplifies to 64/100.
Step 7: Reduce the fraction
Reduce the fraction to its lowest terms, if possible. In this case, we can divide both the numerator and denominator by 4: 64/100 = 16/25.
Therefore, the repeating decimal 0.64 can be represented as the ratio 16/25.
To convert a repeating decimal into a ratio of two integers, we'll use the concept of series in mathematics.
Step 1: Set up the equation
Let x be the repeating decimal. To convert it into a ratio, we can set up the following equation:
x = 0.646464...
Step 2: Multiply by a power of 10
Since the repeating pattern occurs after the decimal point, we will multiply both sides of the equation by 100, which is 10 raised to the power of the number of decimal places in the repeating pattern. In this case, the pattern is two digits long, so we multiply by 100:
100x = 64.646464...
Step 3: Subtract the original equation from the multiplied equation
To eliminate the repeating part, subtract the original equation from the multiplied equation:
100x - x = 64.646464... - 0.646464...
99x = 64
Step 4: Solve for x
Divide both sides of the equation by 99 to isolate x:
x = 64/99
Therefore, the repeating decimal 0.64 can be written as the ratio 64/99.