Number

Write the fraction $\frac{7}{20}$ as a decimal.

Evaluate $14 + (-20)$.

Convert the decimal $0.02$ into a percentage.

Which number is the smallest?

Convert the decimal $0.005$ to a percentage.

Multiply $1.25$ by $0.8$.

Find the fraction that lies exactly halfway between $\frac{1}{4}$ and $\frac{1}{2}$.

In a library, $\frac{4}{9}$ of the books are in English. $60\%$ of the remaining books are in French, and the rest are in Spanish. If there are $720$ more English books than Spanish books, what is the total number of books in the library?

Evaluate $(0.2)^3 + (0.1)^2$.

Find the sum: $\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16}$.

What is the prime factorization of $14$?

What is the LCM of $2, 3,$ and $4$?

Find the HCF of $11$ and $13$.

Express $32$ as a power of its only prime factor.

Find the HCF of $81$ and $243$.

Write $1024$ as a product of prime factors.

Find the smallest number which is exactly divisible by $20$ and $25$.

Find the smallest integer $n > 1$ such that $n$ leaves a remainder of 1 when divided by 2, 3, 4, 5, and 6.

What is the HCF of two consecutive even integers $2n$ and $2n+2$?

How many factors of 120 are also multiples of 4?

Evaluate the expression: $\sqrt{1} + \sqrt{0}$.

Simplify $n^0 \times n^5$.

Simplify $(m^3)^3$.

Find the square root of 225.

Simplify $\frac{x^3 y^2}{(xy)^2}$.

Evaluate $\sqrt{10^4 \div 10^2}$.

What is $(4^2)^{\frac{3}{2}}$?

Simplify $\frac{a^3 \cdot \sqrt[3]{a^2}}{a^{-1/3}}$.

If $x = 2$, evaluate $(x^x)^x$.

Find $x$ given: $2^{x-1} \cdot 4^{x+1} = 8^{x-2}$.

A map is drawn to a scale of $1:50,000$. If the distance between two points on the map is $8\text{ cm}$, calculate the actual distance in kilometers (km).

Simplify the ratio $12:18:30$ to its lowest terms.

Divide $40$ into the ratio $1:3:4$. What are the values?

Solve for $x$: $x:30 = 1:5$.

In a large choir, the ratio of men to women is $5 : 7$. There are $48$ more women than men in the choir. What is the total number of people in the choir?

A fruit punch is made by mixing $450\text{ ml}$ of orange juice with $1.2\text{ liters}$ of lemonade. Express the ratio of orange juice to lemonade in its simplest form.

Six people can clean a stadium in $4$ hours. If the number of people is increased to $8$, how many hours will it take to clean the same stadium, assuming they all work at the same constant rate?

If $x \propto y^3$ and $x=16$ when $y=2$, find $x$ when $y=3$.

A piece of string $120$ cm long is cut into three pieces in the ratio $2:3:5$. Find the length of the longest piece.

In a school, the ratio of teachers to students is $1:20$. If the number of students increases by $100$ and the number of teachers increases by $2$, the new ratio is $1:22$. How many students were there originally?

What is $0.0000006$ in standard form?

Write $80,000$ in standard form.

Express $9.01 \times 10^{-3}$ as a decimal.

Convert $5.77 \times 10^3$ to an ordinary number.

Express $\frac{0.0006 \times 0.002}{0.0004}$ in standard form.

If the speed of a jet is $2.5 \times 10^2$ m/s, how many kilometers does it travel in $1 \times 10^4$ seconds?

Simplify $(4 \times 10^{-3}) \div (8 \times 10^{-5})$ and write in standard form.

Solve $\frac{k}{2 \times 10^5} = 3.5 \times 10^{-8}$ for $k$.

An oil drop has a volume of $2 \times 10^{-12}$ $m^3$. It spreads on water to form a film of thickness $5 \times 10^{-10}$ m. What is the area of the film in standard form?

If $y = 10^6$, express $y^2 + y$ in standard form.

Round $0.0000851$ to $1$ significant figure.

What is the upper bound of $300$ rounded to the nearest $100$?

Estimate the value of $\frac{4.1 + 5.9}{1.8}$ by rounding each to $1$ significant figure.

Round $7,821$ to $2$ significant figures.

If $x = 10$ correct to 1 significant figure and $y = 5$ correct to 1 significant figure, what is the maximum possible value of $\frac{x}{y}$?

Round $9.99$ to 1 significant figure.

A number $k$ is $2.0 \times 10^3$ correct to 2 significant figures. What is the lower bound?

A runner's time for $100 \text{ m}$ (nearest m) is $12.5 \text{ s}$ (1 dp). Calculate the lower bound for their average speed.

The volume of a cone is $V = \frac{1}{3}\pi r^2 h$. If $r = 3 \text{ cm}$ (nearest cm) and $h = 10 \text{ cm}$ (nearest cm), find the upper bound of $V$.

Calculate the upper bound for $z = \frac{1}{x-y}$ if $x = 10$ (nearest 1) and $y = 5$ (nearest 1).