What is 0.13888888888 as a fraction? Tutorial in mathshowcase.info

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 0.13888888888 to a fraction.

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

Often, convert 0.138 to a fraction or 0.139 to a fraction, depending on the task.

Understanding the decimal: “0.13888888888”

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 0.13888888888, 0 is the integer part and 13888888888 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 0.13888888888.
- By removing the decimal point, we derive the numerator as 13888888888.
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.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 13888888888 include 1, 2, 4, 7, 8, 14, 17, 19, 28, 34, 38, 43, 49, 56, 68, 76, 86, 98, 119, 133, 136, 152, 172, 196, 238, 266, 301, 323, 344, 392, 476, 532, 602, 646, 731, 817, 833, 931, 952, 1064, 1204, 1292, 1462, 1634, 1666, 1862, 2107, 2261, 2408, 2551, 2584, 2924, 3268, 3332, 3724, 4214, 4522, 5102, 5117, 5719, 5848, 6536, 6664, 7448, 8428, 9044, 10204, 10234, 11438, 13889, 15827, 16856, 17857, 18088, 20408, 20468, 22876, 27778, 31654, 35714, 35819, 40033, 40936, 43367, 45752, 48469, 55556, 63308, 71428, 71638, 80066, 86734, 96938, 97223, 109693, 111112, 124999, 126616, 142856, 143276, 160132, 173468, 193876, 194446, 219386, 249998, 286552, 303569, 320264, 339283, 346936, 387752, 388892, 438772, 499996, 607138, 678566, 680561, 767851, 777784, 823973, 877544, 999992, 1214276, 1357132, 1361122, 1535702, 1647946, 1864781, 2084167, 2124983, 2374981, 2428552, 2714264, 2722244, 3071404, 3295892, 3729562, 4168334, 4249966, 4749962, 5374957, 5444488, 5767811, 6142808, 6591784, 7459124, 8336668, 8499932, 9499924, 10749914, 11535622, 13053467, 14589169, 14918248, 16673336, 16999864, 18999848, 21499828, 23071244, 26106934, 29178338, 35430839, 40374677, 42999656, 46142488, 52213868, 58356676, 70861678, 80749354, 91374269, 102124183, 104427736, 116713352, 141723356, 161498708, 182748538, 204248366, 248015873, 283446712, 322997416, 365497076, 408496732, 496031746, 730994152, 816993464, 992063492, 1736111111, 1984126984, 3472222222, 6944444444, and 13888888888.
- 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.
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 13888888888 and 100000000000 is 8.

The factors of 13888888888 are:

1 2 4 7 8 14 17 19 28 34 38 43 49 56 68 76 86 98 119 133 136 152 172 196 238 266 301 323 344 392 476 532 602 646 731 817 833 931 952 1064 1204 1292 1462 1634 1666 1862 2107 2261 2408 2551 2584 2924 3268 3332 3724 4214 4522 5102 5117 5719 5848 6536 6664 7448 8428 9044 10204 10234 11438 13889 15827 16856 17857 18088 20408 20468 22876 27778 31654 35714 35819 40033 40936 43367 45752 48469 55556 63308 71428 71638 80066 86734 96938 97223 109693 111112 124999 126616 142856 143276 160132 173468 193876 194446 219386 249998 286552 303569 320264 339283 346936 387752 388892 438772 499996 607138 678566 680561 767851 777784 823973 877544 999992 1214276 1357132 1361122 1535702 1647946 1864781 2084167 2124983 2374981 2428552 2714264 2722244 3071404 3295892 3729562 4168334 4249966 4749962 5374957 5444488 5767811 6142808 6591784 7459124 8336668 8499932 9499924 10749914 11535622 13053467 14589169 14918248 16673336 16999864 18999848 21499828 23071244 26106934 29178338 35430839 40374677 42999656 46142488 52213868 58356676 70861678 80749354 91374269 102124183 104427736 116713352 141723356 161498708 182748538 204248366 248015873 283446712 322997416 365497076 408496732 496031746 730994152 816993464 992063492 1736111111 1984126984 3472222222 6944444444 13888888888

The factors of 100000000000 are:

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 100000000000

Conversion formula (equation):

$0.13888888888 = \frac{0.13888888888}{1} = \frac{0.13888888888 × 100000000000}{1 × 100000000000} = \frac{13888888888}{100000000000} = \frac{13888888888÷8}{100000000000÷8} = \frac{1736111111}{12500000000}$

Solution:

0.13888888888 = $\frac{1736111111}{12500000000}$

What is a decimal?

A decimal is a numeral system that includes a point to separate the whole number part from the fractional part. This system makes it easy to work with numbers less than one.

What is a fraction?

A fraction is a mathematical way of showing a part of a whole. It has two parts: the numerator on top and the denominator below, which help express partial values and comparisons.

Step-by-step solution:

Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 0.13888888888 = $\frac{0.13888888888}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 0.13888888888, 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. $\frac{0.13888888888 × 100000000000}{1 × 100000000000}$ = $\frac{13888888888}{100000000000}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 8. Divide both the numerator and the denominator by this common divisor. $\frac{13888888888 ÷ 8}{100000000000 ÷ 8}$ = $\frac{1736111111}{12500000000}$

Answer in mixed fraction format:

0.13888888888 =

138889

1000000

What is 0.13888888888 as a fraction?