Number

Find the total: $\frac{1}{10} + \frac{2}{10} + \frac{3}{10}$.

Divide $-100 \div 10$.

Calculate $25 - 0.5$.

What is $\frac{1}{3} \div \frac{1}{3}$?

Solve the expression: $2.5 \times (-4) + 15 \div 0.5$.

Evaluate: $\frac{11}{4} - \frac{3}{2} \div \frac{2}{3}$.

Calculate: $|-15| + (-10) - |-5|$.

A technician monitors the internal temperature of a thermal cell. The cell starts at an initial temperature of $15.5^{\circ}C$ and undergoes three consecutive phases of change as described in the table below:

What is the final temperature of the thermal cell after all three phases are completed?

Evaluate the exact value of the following numerical expression:

$\frac{(-0.4)^2 - \frac{1}{20}}{\left(-\frac{2}{5}\right) \times 0.25} + (-2)^3$

Find the value of $P$ if $P = \left( -1 \frac{1}{2} \right) \div 0.5 + 2.4 \times \frac{5}{6}$.

Which of the following expressions has the greatest numerical value?

The estimated number of cells in a specific biological sample is $80,000,000$. Express this value in scientific notation.

Simplify the algebraic expression $w^{1} \times w^{0}$.

Evaluate the result of the subtraction $10^{3} - 10^{2}$.

Light travels at a speed of approximately $3 \times 10^{5}$ km/s. Calculate the distance light travels in $4 \times 10^{2}$ seconds and express the result in scientific notation.

Simplify the expression $\frac{(3^{2})^{4}}{3^{5}}$ and express your answer as a single power of $3$.

Solve the equation $9^{x} = 27$.

In a computational model, the efficiency index $E$ of an algorithm after $n$ iterations is defined by the following power relation:

$E = \frac{(4^{n+1} \times 2^{n-2})^2}{8^{n-1}}$

A programmer finds that for a specific task, the efficiency index is $4096$. The table below provides some powers of $2$ for reference:

Determine the number of iterations $n$ required to reach this efficiency index.

Solve for $n$ if $2^{n-1} \cdot 4^n = 8$.

Evaluate $\frac{2^{-1}}{3^{-1}} + \frac{3^{-2}}{2^{-2}}$.

What is the square root of 256?

Find the value of $x$ if $\sqrt[3]{x} = 4$.

Between which two consecutive integers is $\sqrt{70}$?

Calculate $\sqrt{16} - \sqrt[3]{8}$.

Find the value of $y$ if $y = \sqrt{1.69} + \sqrt[3]{0.001}$.

Between which two integers does $\sqrt[3]{30}$ lie?

Simplify the expression: $\sqrt{100 \times 36}$.

A square has a perimeter of $\sqrt{256}$ cm. Find its area.

If the area of a circle is $121\pi$ square units, what is its radius?

Simplify $\frac{\sqrt{50} + \sqrt{32}}{\sqrt{2}}$.

Convert $0.0101$ to scientific notation.

Express $8.8 \times 10^2$ in standard form.

What is $0.000000405$ in scientific notation?

Write $52,000,000,000$ in scientific notation.

Find the value of $k$ if $(5 \times 10^k) \div (2 \times 10^3) = 2.5 \times 10^{-7}$.

Express the sum $0.004 + (2 \times 10^{-3})$ in scientific notation.

If $a = 2 \times 10^3$ and $b = 3 \times 10^{-5}$, find the value of $a/b$ in scientific notation.

A square has an area of $2.25 \times 10^{14}$ square micrometers. What is the length of its side in meters?

Which of the following is equal to $(5 \times 10^{-4})^{-2}$?

Calculate the value of $\frac{2 \times 10^4 + 3 \times 10^3}{5 \times 10^{-1}}$.

The ratio $3:7$ is equivalent to $15:y$. What is the value of $y$?

If the ratio of boys to girls in a school is $4:5$ and there are $200$ boys, how many girls are there?

In a box of $40$ pens, $25\%$ are red. What is the ratio of red pens to non-red pens?

Express the ratio $80\text{c}$ to $\$2.00$ in simplest form.

A specific type of metal costs $\$1.80$ for $450 \text{ g}$. How much would $1.5 \text{ kg}$ of this metal cost?

Five friends share a prize. The first friend receives $\frac{1}{5}$ of the prize. The remaining four friends share the rest of the money equally. What is the ratio of the first friend's share to any one of the other friends' shares?

A model boat is built to a scale of $1:50$. If the real boat has a length of $15 \text{ meters}$, what is the length of the model boat in centimeters?

Bottle A contains a $20\%$ acid solution and Bottle B contains a $50\%$ acid solution. If the solutions from A and B are mixed in the ratio $2:1$, what is the percentage of acid in the resulting mixture?

Partner A invests $\$1000$ for $12$ months and Partner B invests $\$2000$ for $5$ months in a business. If the total profit is shared in proportion to the product of investment and time, what is the ratio of their profits A:B?

In a sequence of three positive numbers, the ratio of any two consecutive terms is $2:3$. If the sum of the three numbers is $38$, find the middle number.

A car is bought for $\$5,000$ and sold for $\$4,500$. What is the loss percentage?

If the selling price of a chair is $\$120$ and the profit made was $\$20$, what was the cost price?

Calculate $35\%$ of $200$.

A hat's price is reduced from $\$20$ to $\$15$. What is the percentage discount?

If $15\%$ of $200$ is equal to $x\%$ of $60$, find the value of $x$.

After spending $40\%$ of his monthly income on rent and $30\%$ on food, a man has $\$900$ left. What is his total monthly income?

By selling $33$ meters of cloth, a merchant gains a profit equal to the selling price of $11$ meters. Find his gain percentage.

A sum of money at simple interest amounts to $\$815$ in $3$ years and to $\$854$ in $4$ years. The principal sum is:

A man buys oranges at the rate of $3$ for $\$1.40$ and an equal number at the rate of $2$ for $\$1.10$. He sells the whole lot at the rate of $5$ for $\$2.40$. Find his gain or loss percentage.

An article is sold at a loss of $10\%$. Had it been sold for $\$90$ more, there would have been a gain of $5\%$. Find the cost price of the article.

To which of the following number sets does the value $\sqrt{0.64}$ belong?

What is the square root of $1$ classified as?

Which of these is an example of a non-real number?

If a decimal terminates, it must be:

Which of the following is a non-real number?

The set $\{..., -2, -1, 0, 1, 2, ...\}$ represents which number set?

Every natural number is also a:

What set of numbers does $\frac{0}{5}$ belong to?

Classify the number $0.575775777...$ where the number of 7s increases by one in each group.

Which of the following statements is always true?

What is the absolute value of $-1000$?

What is the value of $|-0.1|$?

Find the result of $20 - |-20|$.

Evaluate $|-15| + 5$.

Evaluate the expression: $|-8| + x = 0$. What is the value of $x$?

If $x$ is a negative number, which of the following is equivalent to $|x|$?

Evaluate: $|-2.5| + |-3.5|$.

If $x$ is a number such that $|x| < \sqrt{10}$, how many integers could $x$ possibly be?

What is the largest integer $x$ that satisfies $|3x - 2| \le 10$?

If $|a| = a$ and $|b| = -b$, where $a \neq 0$ and $b \neq 0$, what is the sign of $a \times b$?

Which of these numbers is the $5^{th}$ term of $n^2 - 1$?

Find the common difference in $0.2, 0.4, 0.6, 0.8, \dots$.

What is the next term in the sequence $64, 32, 16, 8, \dots$?

What is the $8^{th}$ term of the sequence $n + 12$?

For the sequence $u_n = 7n - 10$, calculate the $11^{th}$ term.

A sequence follows the rule $u_n = n^3 - 1$. Find the $4^{th}$ term.

Find the next term in the sequence $2, 6, 12, 20, 30, \dots$.

If $u_1 = 3$ and $u_{n+1} = u_n^2 - 5$, find the value of $u_3$.

Find the $n$-th term formula for the sequence: $-1, 2, 7, 14, 23, ...$

The $n$-th term of a sequence is $u_n = (n-5)(n-10)$. For which values of $n$ is the term equal to 0?

Simplify $6^7 \div 6$.

Simplify $(x^2)^4 \div x^3$.

Simplify $y^4 \times y^{-4}$.

What is the value of $(\frac{3}{4})^0$?

Evaluate the expression $\frac{3^{-1} - 3^{-2}}{3^{-3}}$.

Simplify $2^x \cdot 2^y \div 2^z$.

Simplify the expression $x^{1/2} \times x^{1/2}$ (using the product law).

If $2^x = 3^y = 6^{-z}$, find the value of $\frac{1}{x} + \frac{1}{y} + \frac{1}{z}$.

Simplify $\frac{(x+1)^{-1} - (x-1)^{-1}}{2}$ .

Solve for $x$: $10^{x+1} = 0.01 \cdot 100^{x}$ .

Simplify the expression: $\sqrt{4} + \sqrt{9} + \sqrt{16}$

Calculate: $\sqrt{225}$

Simplify the expression: $4\sqrt{2} \times \sqrt{3}$

Simplify: $\sqrt{125}$

Simplify the expression $\sqrt{125}$ into the form $a\sqrt{b}$.

Rationalize the denominator of $\frac{7}{3 + \sqrt{2}}$.

Simplify $4\sqrt{18} - 2\sqrt{32}$.

A right-angled triangle and a square are defined by the measurements in the table below:

Calculate the perimeter of the square. Express your answer in its simplest surd form $a\sqrt{b}$.

Simplify $(3\sqrt{2})^2 - (2\sqrt{3})^2$.