Tag: non-terminating recurring decimals in rational numbers

If $x$ and $y$ are positive number and $x>y$, then 

$9\dfrac{7}{20}= \dfrac{187}{20}=9.35$

$81.472 km = 81472$ meters $= 81500$ meters with three significant digits.
$\displaystyle \therefore Error\%=\frac{81500-81472}{81472}\times 100=0.034\%$

${a}^{2} + {b}^{2} + {c}^{2} = 1 \quad \left( \text{Given} \right)$

$x = 0.d25 d25d25 -----$
$x = 0.\overline{d25}$
$1000 x = d25. \overline{d25}$
$999 x = d 25$
$x = \displaystyle \frac{d 25}{999}$
$x = \displaystyle \frac{d25}{37.27}$
take d = 9 then $x = \displaystyle \frac{25}{27}$
$d = 9          n = 25$
$d + n = 34$

$\dfrac {5}{13} = 0.3846$

(d) is the correct choice.

The term significant figures are referring to the number of important digits (0 through 9 inclusive) in the coefficient of some expression in the scientific notation. The number of significant figures in any expression indicate the confidence or precision with which we can state a quantity.

Some rules for significant figures are:

1. All non-zero numbers are significant.

2. Zeros located between non-zero digits are significant.

3. Trailing zeros at the end will be significant only if the number contains a decimal point; otherwise, they are insignificant.

4. Zeros to the left of the first nonzero digit are insignificant.

5. Number in exponents (for example power of 10) is insignificant.

Thus option D is correct.