Question

A student estimates the weight of astronauts on the moon by multiplying their weight by the decimal 0.16666....what fraction can be used for the same estimation?

Answer 1

`(1)/(6)`

Explanation:

0.16666 can be written as
`(16666)/(1000000)`

write the numerator and denominator as the product of their prime numbers

and divide the common numbers. Thus, it can be further reduced to
`(1)/(6)`

The gravity of moon is about
`(1)/(6)` times the gravity of the Earth due to which the weight of the astronauts on the moon can be found by multiplying by the decimal 0.16666.. or
`(1)/(6)`.

Answer 2

Let
`x = 1.66666...` ....(1)

Multiply both sides of equation (1) by 10.

`10x = 1.666666....` .... (2)

Multiply both sides of equation (1) by 100.

`100x = 16.66666....`... (3)

Subtract equation (2) from equation (3)

`100x - 10x = 16.66666...- 1.66666...`

`90x = 15`

`x= (15)/(90)  = (1)/(6)`

Hence, the required fraction form is
`(1)/(6)` .... Answer.