Hello.\u00a0 What rain yesterday, here in Campbell River!\u00a0 Well, we sure needed it.\u00a0 It’s nice to have more seasonal temperatures after the oven that was last week.<\/p>\n
A math tutor often encounters the topic of converting decimals to fractions.\u00a0 Terminating decimals are easy:\u00a0 for instance, 0.9 is 9\/10.\u00a0 Then, 0.31 is just 31\/100.\u00a0 As well, 0.222 is 222\/1000, which reduces to 111\/500.<\/p>\n
What about repeating decimals, such as 0.333333…….?<\/p>\n
Well, there’s an algebraic trick for that:<\/p>\n
Let x=0.3333…..(Note that x=1x; we just don’t usually write the one.)<\/p>\n
Then<\/p>\n
10x=3.33333……(1)<\/p>\n
1x =0.33333……(2)<\/p>\n
Subtracting (2) from (1) gives 9x=3.00000<\/p>\n
Of course, 3.00000…. = 3, so 9x=3<\/p>\n
Next, divide both sides by 9 to isolate x:<\/p>\n
x=3\/9=1\/3<\/p>\n
Recall, we began by defining<\/em> x as 0.333333…..Now, since we see x is also equal to 1\/3, we know that it must be true:<\/p>\n 0.33333……=1\/3<\/p>\n Have a great day, and come back for more hints.<\/p>\n