show that the following decimals rational:

1. 0,124 (the dot is on 1 and 4)

1 answer

To show that the decimal 0.124 is rational, we need to demonstrate that it can be expressed as a fraction of two integers.

We can rewrite the decimal 0.124 as follows:

0.124 = 1/10 + 2/100 + 4/1000

In general, a decimal can be expressed as a sum of fractions with denominators equal to powers of 10. In this case, we have fractions with denominators of 10, 100, and 1000.

Combining these fractions, we get:

0.124 = (1/10) + (2/100) + (4/1000)
= (100/1000) + (20/1000) + (4/1000)
= (100 + 20 + 4)/1000
= 124/1000

Therefore, we have expressed the decimal 0.124 as the fraction 124/1000, which shows that it is rational.