整數、小數與分數：練習題

Which of the following values is equivalent to the fraction \(\frac{3}{5}\)?

Work out the value of \(125^{\frac{2}{3}}\).

Rationalise the denominator of the following expression:
\(\frac{10}{\sqrt{5}}\)

Express \(0.000045\) in standard form.

A map has a scale of \(1:25000\).
The distance between two villages on the map is 8 cm.
What is the actual distance between the villages in kilometres?

Write \(60\) as a product of its prime factors.
Give your answer in index form.

Work out the value of \( (2^3)^2 \times 5^0 \).

Calculate \(0.4 \times 0.2\).

A recipe for 6 people uses 900 g of flour and 120 g of sugar.

a) Work out how much flour is needed for 10 people.
b) Work out how much sugar is needed for 10 people.
c) Sarah has 1.4 kg of flour and 200 g of sugar. Does she have enough ingredients to make the recipe for 10 people? You must show your working and explain your answer.

(a) Show that the recurring decimal \(0.2\dot{3}\dot{6}\) can be written as the fraction \(\frac{13}{55}\).
(b) Given that \(y\) is inversely proportional to the square of \(x\), and \(y = 10\) when \(x = 3\):
(i) Express \(y\) in terms of \(x\).
(ii) Calculate the value of \(y\) when \(x = 5\).
(c) Simplify \((3 \times 10^5) \times (4 \times 10^{-2})\), giving your answer in standard form.