Convert the following repeating decimal to a fraction in simplest form.
point, start overline, 01, end overline
.
01
‾
.
01
Let's call the repeating decimal x.
If we take away the repeating part, we get:
10x = 0.01
If we move the decimal point two places to the right, we get:
100x = 1
Now we can subtract the two equations:
100x - 10x = 1 - 0.01
90x = 0.99
To get x by itself, we divide both sides of the equation by 90:
x = 0.99 / 90
Simplifying the fraction:
x = 11 / 1000
Therefore, the repeating decimal 0.01 with a line over the "01" can be written as the fraction 11/1000.
Convert the following repeating decimal to a fraction in simplest form.
point, start overline, 01, end overline
.
_
01
.
01
Let's call the repeating decimal x.
If we take away the repeating part, we get:
100x = 0.01
If we move the decimal point two places to the right, we get:
10000x = 1
Now we can subtract the two equations:
10000x - 100x = 1 - 0.01
9900x = 0.99
To get x by itself, we divide both sides of the equation by 9900:
x = 0.99 / 9900
Simplifying the fraction:
x = 1 / 100
Therefore, the repeating decimal 0.01 with a line over the "01" can be written as the fraction 1/100.
Alternatively, if we observe that the repeating decimal is 0.01010101..., we can write it as a geometric series:
0.01010101... = 0.01 * (1 + 0.01 + 0.0001 + ...)
Using the formula for the sum of an infinite geometric series:
Sum = a / (1 - r)
where "a" is the first term and "r" is the common ratio, we can substitute in the known values:
Sum = 0.01 / (1 - 0.01) = 0.01 / 0.99
Simplifying the fraction:
0.01 / 0.99 = 1/100
Therefore, the repeating decimal 0.01 with a line over the "01" can also be written as the fraction 1/100.
Convert the following repeating decimal to a fraction in simplest form.
point, 8, start overline, 5, end overline
.
8
5
‾
.8
5
Let's call the repeating decimal x.
If we take away the repeating part, we get:
10x = 8.85
If we move the decimal point two places to the right, we get:
100x = 88.5
Now we can subtract the two equations:
100x - 10x = 88.5 - 8.85
90x = 79.65
To get x by itself, we divide both sides of the equation by 90:
x = 79.65 / 90
Simplifying the fraction:
x = 8865 / 9900
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 15:
x = 591 / 660
Therefore, the repeating decimal 8.85 with a line over the "85" can be written as the fraction 591/660.
To convert the repeating decimal to a fraction, we can use the following steps:
Step 1: Let x be the given repeating decimal.
x = 0.01‾
Step 2: Multiply both sides of the equation by 100 to remove the decimal points.
100x = 1‾
Step 3: Subtract the original equation from the equation in step 2.
100x - x = 1‾ - 0.01‾
99x = 0.99
Step 4: Divide both sides of the equation by 99 to isolate x.
x = 0.99 / 99
x = 0.01
Step 5: Since the repeating decimal pattern is 0.01‾ and it has only two digits, the repeating portion is over two 9's (99).
x = 0.01 / (99)
Therefore, the repeating decimal 0.01‾ is equal to the fraction 0.01 / 99, which is already in its simplest form.
To convert a repeating decimal to a fraction, we need to follow these steps:
Step 1: Let's assign a variable to the repeating decimal. In this case, let's use x.
So we have x = 0.01‾.
Step 2: Multiply both sides of the equation by a power of 10 that eliminates the repeating part. Since there are two digits repeating, we'll multiply by 100.
100x = 1.01‾.
Step 3: Subtract the original equation from the new equation to eliminate the repeating part.
100x - x = 1.01‾ - 0.01‾,
99x = 1.
Step 4: Solve for x by dividing both sides of the equation by 99.
x = 1/99.
Therefore, the fraction that represents the repeating decimal 0.01‾ is 1/99 in simplest form.