Write each repeating decimal as the sum-of two fractions.
Find the sum and simplify. Verify .
0.75483 =
0.127 =
seems a bit vague
.127 = 127/999 = 99/999 + 37/999 = 11/111 + 1/27
But there are many other ways it can be split up. Same for any other fraction.
To write a repeating decimal as the sum of two fractions, we can use the concept of geometric series.
1. For the number 0.75483, we can first identify the repeating part. In this case, the repeating part is 483.
2. Let's call the repeating part "x". In this case, x = 483.
3. Next, we need to determine the number of digits in the repeating part, which we'll call "n". In this case, n = 3.
4. To get the fraction form, we'll use the formula for the sum of an infinite geometric series:
Sum = x / (10^n - 1)
Plugging in the values, we get:
Sum = 483 / (10^3 - 1)
= 483 / (1000 - 1)
= 483 / 999
Therefore, 0.75483 can be written as the sum of two fractions: 483/999.
To find the sum and simplify it, we can add the two fractions together:
0.75483 = 483/999
To add fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 999 and 1 is 999.
Then, we can rewrite 483 as a fraction with the common denominator:
483/999 + 0/999 = 483/999
Therefore, the sum is 483/999.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 483 and 999 is 3.
Dividing both the numerator and denominator by 3, we get:
483/999 = (483/3) / (999/3) = 161/333
So, the simplified sum is 161/333.
To verify the result, we can calculate the decimal value of 161/333 using a calculator:
161 รท 333 = 0.483
For the number 0.127, there is no repeating part, so it is not a repeating decimal. Therefore, there are no fractions that can represent it as the sum of two fractions.