How do you covert a decimal equivalent that's less than 1 to a fraction?

Answer 1

If the number is a terminated or a repeated decimal (a rational number), you can convert it to a fraction (integer/integer ≠ 0).

If the number is irrational, it's very hard to turn it into a fractional form.

Examples:

1) 0.5 = 5/10 = 1/2

2) 0.234 = 234/1000 = 117/500

3) 0.666... = ? you need to work a little bit.

let x = 0.666... multiply both sides by 10

10x = 6.666...subtract the 1st equation from the 2nd one

9x = 6 divide both sides by 9

x = 6/9 simplify

x = 2/3

thus, 0.666... = 2/3

4) 0.123123... = ? work in the same way as in the problem (3)

let x = 0.123123... multiply both sides by 1,000

1,000x = 123.123123...subtract the 1st equation from the 2nd one

999x = 123 divide both sides by 999

x = 123/999 simplify

x = 41/333

thus, 0.123123... = 41/333

5) 0.343636... = ?

Let 0.343636... = 0.34 + 0.003636... convert them separately into a fraction and add those fractions together.

0.34 = 34/100 = 17/50

let x = 0.003636... multiply both sides by 10,000

10,000x = 36.3636...subtract the 1st equation from the 2nd one

9999x = 36 divide both sides by 9999

x = 36/9999 simplify

x = 4/1111

Thus,

0.343636... = 17/50 + 4/1111 = (17*1111 + 4*50)/(50*1111) = 19,087/55550.

An example of an irrational number written as a fraction:

cos pi/6 ≈ 0.8660254038 = √3/2