What is 0.16666666666 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.16666666666 to a fraction.

You can try other values to get more familiar with the conversion process.

Often, convert 0.1666666 to a fraction or 0.16666666666667 to a fraction, depending on the task.

Understanding the decimal: “0.16666666666”

A decimal number consists of an integer part and a fractional part, separated by a decimal point. The integer part is on the left, and the fractional part is on the right. For example, in 0.16666666666, 0 is the integer part and 16666666666 is the fractional part.

Conversion Explanation:

1. For the numerator:
   • We start with the number 0.16666666666.
   • By removing the decimal point, we derive the numerator as 16666666666.
2. For the denominator:
   • Each position after the decimal represents a division by 10.
   • Thus, having 11 positions after the decimal equates to 100000000000 or 10¹¹.
3. Factors:
   • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
   • For instance, the factors of 16666666666 include 1, 2, 13, 26, 7477, 14954, 85733, 97201, 171466, 194402, 1114529, 2229058, 641025641, 1282051282, 8333333333, and 16666666666.
   • The factors of 100000000000 comprise 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 5000, 5120, 6250, 6400, 8000, 10000, 10240, 12500, 12800, 15625, 16000, 20000, 25000, 25600, 31250, 32000, 40000, 50000, 51200, 62500, 64000, 78125, 80000, 100000, 125000, 128000, 156250, 160000, 200000, 250000, 256000, 312500, 320000, 390625, 400000, 500000, 625000, 640000, 781250, 800000, 1000000, 1250000, 1280000, 1562500, 1600000, 1953125, 2000000, 2500000, 3125000, 3200000, 3906250, 4000000, 5000000, 6250000, 6400000, 7812500, 8000000, 9765625, 10000000, 12500000, 15625000, 16000000, 19531250, 20000000, 25000000, 31250000, 32000000, 39062500, 40000000, 48828125, 50000000, 62500000, 78125000, 80000000, 97656250, 100000000, 125000000, 156250000, 160000000, 195312500, 200000000, 250000000, 312500000, 390625000, 400000000, 500000000, 625000000, 781250000, 800000000, 1000000000, 1250000000, 1562500000, 2000000000, 2500000000, 3125000000, 4000000000, 5000000000, 6250000000, 10000000000, 12500000000, 20000000000, 25000000000, 50000000000, and 100000000000.
4. Greatest Common Divisor (GCD):
   • It's the largest number that can evenly divide both the numerator and the denominator.
   • In this instance, the GCD for 16666666666 and 100000000000 is 2.

The factors of 16666666666 are:

The factors of 100000000000 are:

Conversion formula (equation):

Solution:

Step-by-step solution:

• Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 0.16666666666 = $\frac{0.16666666666}{1}$
• Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.16666666666, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 10¹¹ = 100000000000
• Step 3: Using this factor, multiply both the numerator and the denominator. $\frac{\mathrm{0.16666666666\; \times \; 100000000000}}{\mathrm{1\; \times \; 100000000000}}$ = $\frac{16666666666}{100000000000}$
• Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 2. Divide both the numerator and the denominator by this common divisor. $\frac{\mathrm{16666666666\; ÷\; 2}}{\mathrm{100000000000\; ÷\; 2}}$ = $\frac{8333333333}{50000000000}$

Answer in mixed fraction format:

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