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# How to work this out without calculator? watch

1. Hey guys what is the quickest way to tackle the following question without a calculator.

I feel like im being really stupid right now, my approximation was 0.3 but the mark scheme gave the answer to 1dp as 0.31.

2. (Original post by Shaanv)
Hey guys what is the quickest way to tackle the following question without a calculator.

I feel like im being really stupid right now, my approximation was 0.3 but the mark scheme gave the answer to 1dp as 0.31.

Express it as a fraction first. It's which can be split into and the decimal of the first term should be obvious, then take it and halve it twice.
3. (Original post by Shaanv)
Hey guys what is the quickest way to tackle the following question without a calculator.

I feel like im being really stupid right now, my approximation was 0.3 but the mark scheme gave the answer to 1dp as 0.31.

since it's a small number then multiply by 10 and simplify and then do long division
4. (Original post by Shaanv)
Hey guys what is the quickest way to tackle the following question without a calculator.
Rather than include a massive image, you could have just written 1/3.2.

I think the quickest way to do this is to rewrite as 10 / 32, which is 10 / (2 x 2 x 2 x 2 x 2). So halve 10 five times and you'll get the right answer. If you have any familiarity with fractions you should be able to get to 1.25 after the 3rd halving mentally, then it's just a couple of steps by hand.

Even quicker ways you could use if you happened to know certain useful numbers.

The square root of 10 is around 3.16, so 10/3.16 = 3.16. A small change will affect both numbers by roughly the same amount but in opposite directions, so 10/3.2 will be approximately 3.16 - 0.04 or 3.12 and so 10/32 is approx 0.312

I happen to know that 5^5 is 3125. The fraction you have is 5^5 / 10 ^ 4, or 0.3125

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