2.3 repeating as a fraction is equal to 23/10. To find this, we can use the long division method.
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What is 2.3 repeating as a fraction?
2.3 repeating is a fraction, specifically the fraction 23/100. Because the 3 is repeating, it indicates that the decimal goes on forever, making this an infinite decimal. When converting an infinite decimal to a fraction, you simply need to put the digits that repeat over and over again in the numerator (top part of the fraction) and write “00” in the denominator (bottom part of the fraction). So, in this case, you would write “23” over “100”.
How to convert 2.3 repeating to a fraction
To convert 2.3 repeating to a fraction, you need to understand what repeating decimals are and how to convert them. A repeating decimal is a decimal number that has a digit or digits that repeat endlessly. For example, 0.3333… repeats the digit 3 endlessly, so it’s a repeating decimal. To convert a repeating decimal to a fraction, you need to find the pattern in the decimal and express it as a fraction.
In the case of 2.3 repeating, the pattern is that the digits 2 and 3 repeat endlessly. So, you would express 2.3 repeating as the fraction 23/100.
What is the simplest form of 2.3 repeating?
2.3 repeating is simply 2.3 recurring. In other words, the 3 repeats infinitely.
To convert 2.3 repeating into a fraction, we need to express it as an infinite series:
2.3 = 2 + 0.3 + 0.03 + 0.003 + …
We can then turn this into a fraction by taking the sum of all the terms:
2.3 = 2 + 3/10 + 3/100 + 3/1000 + … = 23/10 + 33/100 + 33/1000 + …
Now we need to cancel out any common factors between the numerator and denominator. 23 and 33 have a common factor of 3, so we can cancel that out:
2.3 = 23/10 + 33/100 + 33/1000 + … = 23/10 + 1/10 + 1/1000 + … = (23+1+1)/10 = 25/10
Therefore, 2.3 repeating is equivalent to 25/10, or 2 1/2 in simplest form.
What is the decimal equivalent of 2.3 repeating?
To convert a decimal to a fraction, we place the decimal number over its place value. For example, in the decimal number 12.345, the 5 is in the thousandths place. So, we would say that 12.345 is equal to the fraction 12345/10000.
When a decimal repeats its digits endlessly, we can use a bar above the digits to signify that they repeat. For example, the fraction 3/10 can be written as 0.3 because 3 repeating is equal to 0.333…. Since 3 is in the tenths place, we can also write 0.3 as 30/100.
Now that we know how to convert a repeating decimal to a fraction, let’s try converting 2.3 repeating to a fraction. We can see that 2.3 repeating is equal to 23/10 because 2 repeating is equal to 0.2 and 3 is in the tenths place. So, we can write 2.3 repeating as 23/10 or 230/100 or 2300/1000, etc.
How to multiply fractions with 2.3 repeating
To multiply fractions with 2.3 repeating, first convert the repeating decimal to a fraction. The easiest way to do this is to use division. For 2.3 repeating, divide 2.3 by 1 and put the answer over 1 with the 2.3 as the numerator and 1 as the denominator:
2.3/1 = 2.3
Now that you have your fraction, multiply it by the other fraction like you would normally multiply fractions:
2.3/1 x 4/5 = 9.2/5
How to divide fractions by 2.3 repeating
To divide fractions by 2.3 repeating, simply invert the number and multiply as usual.
In other words, the answer to “what is 2.3 repeating as a fraction?” is 1/2.3, which can be written as 1/(2.3).
Here’s how it works:
1/(2.3) = (1/2.3) * (1/1) = 1 * (1/1) / (2.3 * 1) = 1/2.3