Word Problems Question Bank #19 quick estimation

[caitlinfitz10]

In evaluating the second statement for word problems question bank #19, I get that you need to multiply .9 x .9 x .9 etc several times to test the probability at different points. However the explanation simply says .9 x .9 x .9 x .9 x .9 x .9 x .9 is approximately 48%. Is there a simple fact to memorize or an approximation to use that would get one to this answer without multiplying it all out? I suppose one could have 9^7 memorized... but I have been making flashcards for these sorts of things to memorize and so far in the strategy guides I haven't seen powers of 9 past like 3 as suggested to memorize... Thanks!

[jnelson0612]

In evaluating the second statement for word problems question bank #19, I get that you need to multiply .9 x .9 x .9 etc several times to test the probability at different points. However the explanation simply says .9 x .9 x .9 x .9 x .9 x .9 x .9 is approximately 48%. Is there a simple fact to memorize or an approximation to use that would get one to this answer without multiplying it all out? I suppose one could have 9^7 memorized... but I have been making flashcards for these sorts of things to memorize and so far in the strategy guides I haven't seen powers of 9 past like 3 as suggested to memorize... Thanks!

Good question! You don't have to memorize this information; you just need to estimate. Here's how I would do it:

.9 * .9 is about .8 (9*9=81)
.8 * .9 is about .7
.7 * .9 is about .6
.6 * .9 is about .54
.54 * .9 is about .48 (once I get to the one I'm most interested in I would keep the hundredths place. You can see that I dropped them on the first few because they tended to be close to 0, so I just rounded down.)

Please let me know if you would like any further clarification. :-)

[caitlinfitz10]

Hi Jamie,

Thanks for your reply! I'm sorry but I'm still a bit confused. Isn't .54 x .9 equal to .6 x .9 x .9? How do you know that that is about the same as .9 x .9 x .9 x .9 x .9 x .9 x .9? Thanks!

[jnelson0612]

Hi Jamie,

Thanks for your reply! I'm sorry but I'm still a bit confused. Isn't .54 x .9 equal to .6 x .9 x .9? How do you know that that is about the same as .9 x .9 x .9 x .9 x .9 x .9 x .9? Thanks!

Shoot, Caitlin, you are right! Ack!

Okay, then here's what I did. I know that .9*.9 is .81. I just quickly multiplied together .81 and .81. I got .6561. Then I multiplied that by .81 again. I got .5313. I timed myself and it took less than 10 seconds to do all of this, so it's doable.

That takes care of six .9s. I have one more .9 to multiply by. I know that I'm going to end up reducing .531 by 10%, or subtracting about .053. That gives me a number a little less than .48.

I think the takeaway here is to go ahead and crunch out the math to avoid the trap that I fell into. :-)