But how does 0.2 convert to 1/5?

2 Answers
Apr 4, 2018

#0.2=2/10=1/5#

Explanation:

#0.2# is two-tenths, which is #2/10#. Reduce #2/10# to #1/5#.

Apr 4, 2018

#0.2=2/10=1/5#

Explanation:

To convert from decimals to fractions, divide numbers in the tenths place (e.g. 0.7) by ten, numbers in the hundredths place (e.g. 0.45, 0.03, etc.) by one hundred, and so on. A more "mathematical" approach is to multiply the decimal by a power of ten for every number after the decimal (e.g. #0.45 *100 = 45#), divide by that power of ten (e.g. #45/100#), then reduce (#45/100=9/20#). For 0.2, the tenths place, 2, is divided by 10: #2/10#, which reduces to #1/5# (alternatively, #(0.2*10)/10=2/10=1/5#).

To convert from fractions to decimals, use division. For #1/5#, divide 1 by 5 (demonstrating long division is kind of difficult on Socratic, however) which equals 0.2. (Other examples: #3/7 = 0.4286#, #9/8 = 1.125#)