Decimals and Fractions
- You can convert between decimals and fractions
- A terminating fraction is one that ends.
- A recurring fraction is one which has one or more repeating digits.
- All fractions can be changed into a decimal To work out if a fraction will be represented by a terminating or a recurring decimal:
- If any of these prime factors are only 2s or 5s then the fraction will convert to a terminating fraction.
- If any prime number other than 2 or 5 is present then the fraction will convert to a recurring decimal.
E.G. Is this fraction terminating or recurring?
9/96 ----> simplify = 3/32 ----> Prime factors = 2 ----> T/R = Terminating
- Know that a recurring decimal is and extact fraction.
- Change recurring decimals into exact fractions.
r = recurring
E.G. Change 0.3r into an exact fraction:
(10x = 3.3r) - (x = 0.3r) = 9x = 3 / 9 = x = 3/9 = 1/3
- You can round a number correct to a given number of significant figures.
When working out an estimate for a value of an expression (or otherwise) round each number correct to one significant figure.
E.G. Calculate an estimate:
(9.8 x 3.9) / 0.14 aprox = (10 x 4) / 0.1 = 40 / 0.1 = 400
This is an overestimate as the numerators have both been rounded up. The demoninator has been rounded down, so when we divide, our answer is even bigger.