Please, can u convert 3.16 (6 repeating) to a fraction.

Question

Chanell Sanborn · Accepted Answer

10x=31.666…&amp;nbsp;9x=10x−x&amp;nbsp;9x=31.666..−3.1666…&amp;nbsp;9x=28.5&amp;nbsp;x=28.59=28590=196=316

vrangett · Accepted Answer

3.1666…=316 as a fraction.

Accepted Answer

3.2 repeating as a fraction&amp;nbsp;

Jeffrey Jordon · Accepted Answer

Answer:196Explanation:To convert the decimal number 3.166666... to a fraction, we can use the following method:Let x=3.166666.... Then, we can write:10x=31.666666...Subtracting the left-hand side from the right-hand side, we get:9x=28.5Dividing both sides by 9, we get:x=28.59=5718Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:5718=196Therefore, the decimal number 3.166666... can be expressed as the fraction 196.

RizerMix · Accepted Answer

Let x=3.166666.... Then, we can write:x=3.16+0.006666...Notice that the decimal 0.006666... is repeating, and we can represent it as a fraction by putting it over a power of 10 with the same number of digits as the repeating block. In this case, we have:0.006666...=6900=1150Substituting this back into the equation for x, we get:x=3.16+1150Now, we can convert the decimal 3.16 to a fraction by multiplying it by 100/100, which gives:3.16=316100Substituting this back into the equation for x, we get:x=316100+1150To add these two fractions, we need to find a common denominator. The smallest number that both 100 and 150 divide into is 300, so we can write:x=316·3100·3+1·2150·2Simplifying each fraction, we get:x=948300+2300Combining the two fractions, we get:x=950300Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 50:x=950300=196Therefore, the decimal number 3.166666... can also be expressed as the fraction 196, using a different method.

Convert 3.16 (6 repeating) to a fraction.

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