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

Answer:

$\frac{1}{6}$      

Step-by-step explanation:

0.16666 can be written as $\frac{16666}{1000000}$

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

and divide the common numbers. Thus, it can be further reduced to $\frac{1}{6}$

The gravity of moon is about $\frac{1}{6}$ 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 $\frac{1}{6}$.

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)

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

$90x = 15$

$x= \frac{15}{90} = \frac{1}{6}$

Hence, the required fraction form is $\frac{1}{6}$ .... Answer.