Express 6.455 correct to 1 d.p., 2 s.f., nearest whole number, and express 0.52 as a common fraction in simplest form.

To round to 1 decimal place, we look at the second decimal digit. If it is 5 or greater, we round up the first decimal digit.
The second decimal digit in 6.455 is 5.
So, we round up the first decimal digit (4) to 5.

$$6.455 \approx 6.5$$

To round to 2 significant figures, we look at the third significant digit. If it is 5 or greater, we round up the second significant digit.
The first significant digit is 6, the second is 4. The third significant digit is 5.
So, we round up the second significant digit (4) to 5.

$$6.455 \approx 6.5$$

To round to the nearest whole number, we look at the first decimal digit. If it is 5 or greater, we round up the whole number part.
The first decimal digit in 6.455 is 4. Since $4 < 5$, we keep the whole number part as it is.

$$6.455 \approx 6$$

First, write the decimal as a fraction:

$$0.52 = \frac{52}{100}$$

Next, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor. Both 52 and 100 are divisible by 4.

$$\frac{52 \div 4}{100 \div 4} = \frac{13}{25}$$

The fraction $\frac{13}{25}$ is in its simplest form because 13 is a prime number and 25 is not a multiple of 13.

a)

i) $\boxed{6.5}$

ii) $\boxed{6.5}$

iii) $\boxed{6}$

b) $\boxed{\frac{13}{25}}$