Radicals and Scientific Notation

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Questions and Answers

Which of the following pairs are considered 'like radicals'?

$2\sqrt{3}$ and $\sqrt{12}$ (correct)
$\sqrt{11}$ and $7$
$\sqrt{5}$ and $\sqrt{7}$
$3\sqrt{2}$ and $2\sqrt{3}$

If you simplify $\sqrt{18} + \sqrt{32}$, what is the resulting expression?

$5\sqrt{5}$
$7\sqrt{2}$ (correct)
$7\sqrt{5}$
$5\sqrt{2}$

Simplify the following expression: $2\sqrt{27} - \sqrt{12} + \sqrt{75}$

$8\sqrt{3}$
$9\sqrt{3}$ (correct)
$6\sqrt{3}$
$10\sqrt{3}$

Which of the following expressions can be simplified into a single radical term?

$\sqrt{20} - \sqrt{5}$ (C) Signup and view all the answers

What is the simplified form of $\frac{1}{3}\sqrt{18} + \frac{1}{2}\sqrt{32} - \sqrt{2}$?

$2\sqrt{2}$ (A) Signup and view all the answers

Which of the following numbers is correctly expressed in scientific notation?

4.6 × 10^5 (A) Signup and view all the answers

If a calculator displays `9.14 07`, what number is being represented?

91,400,000 (B) Signup and view all the answers

What is the ordinary decimal notation of $3.09 × 10^{-6}$?

0.00000309 (C) Signup and view all the answers

Which of the following represents the number 0.0000416 in scientific notation?

4.16 × 10^-5 (D) Signup and view all the answers

A computer displays a number as `3.8 E-05`. What is the ordinary decimal notation of this number?

0.000038 (B) Signup and view all the answers

What is the result of rounding the number 38,499 to the nearest 1000 and the nearest 100?

39,000 and 38,500 (C) Signup and view all the answers

When approximating a number to a certain number of decimal places, which digit determines whether the last digit to be written should be rounded up?

The digit immediately to the right of the last digit. (A) Signup and view all the answers

What is 9.995 approximated to 2 decimal places?

10.00 (C) Signup and view all the answers

What does approximating a number to 2 decimal places mean?

Approximating the number to the nearest hundredth. (A) Signup and view all the answers

In the number 123.45, which digit is the most significant and which is the least significant?

1 is most significant, 5 is least significant (C) Signup and view all the answers

How many significant figures are there in the number 0.00805?

3 (A) Signup and view all the answers

What is 0.0674 rounded to 2 significant figures?

0.068 (C) Signup and view all the answers

Which property is demonstrated by the following equation? $\frac{-7}{9} (\frac{3}{2} + \frac{-4}{5}) = \frac{-7}{9} (\frac{-4}{5} + \frac{3}{2})$

Commutative property of addition (C) Signup and view all the answers

Simplify the following expression: $\frac{3}{7} + (\frac{5}{6} + \frac{-3}{7})$

$\frac{5}{6}$ (C) Signup and view all the answers

What is 149,999 rounded to 3 significant figures?

150,000 (D) Signup and view all the answers

Which of the following expressions illustrates the associative property of multiplication?

$\frac{2}{3} \times (\frac{3}{2} \times \frac{5}{9}) = (\frac{2}{3} \times \frac{3}{2}) \times \frac{5}{9}$ (B) Signup and view all the answers

If $x$ and $y$ are rational numbers, and $x < y$, which of the following statements is always true?

There are infinitely many rational numbers between $x$ and $y$. (D) Signup and view all the answers

Evaluate the expression: $\frac{-9}{7} \times (\frac{-23}{27}) \times \frac{-7}{9}$

$\frac{23}{243}$ (C) Signup and view all the answers

Simplify the following expression using the properties of exponents: $\frac{10^5}{10^1}$

$10^4$ (B) Signup and view all the answers

A rectangle has an area of $223.2 \text{ cm}^2$ and a width of $8.4 \text{ cm}$, both measured to 1 decimal place. What is the upper bound for the length $x$?

$26.66 \text{ cm}$ (D) Signup and view all the answers

If $a$ and $b$ are real numbers such that $a^5 \times a^2 = a^x$, and $\frac{b^7}{b^3} = b^y$, what are the values of $x$ and $y$?

$x = 7$, $y = 4$ (D) Signup and view all the answers

Which of the following is equivalent to $(\frac{1}{2})^4 ÷ (\frac{1}{2})^2$?

$\frac{1}{4}$ (B) Signup and view all the answers

A rectangle has a length of $109.7 \text{ m}$ and a width of $48.8 \text{ m}$, both measured to 1 decimal place. What is the lower bound for the perimeter of the rectangle?

$317.0 \text{ m}$ (C) Signup and view all the answers

Which of the following numbers is NOT written in scientific notation?

$0.99 \times 10^{2}$ (A) Signup and view all the answers

By what power of 10 must you multiply 2.1 to get 21000?

$10^4$ (D) Signup and view all the answers

Which expression correctly represents 0.000056 in scientific notation?

$5.6 \times 10^{-5}$ (D) Signup and view all the answers

If multiplying a number by $10^{-n}$ moves its decimal point 4 places to the left, what is the value of $n$?

4 (C) Signup and view all the answers

Which of the following represents the result of dividing $6.3 \times 10^5$ by $9 \times 10^2$?

$7 \times 10^2$ (B) Signup and view all the answers

What value of $x$ would make the number $0.x5 \times 10^3$ be correctly expressed in scientific notation?

Any non-zero digit (C) Signup and view all the answers

What distinguishes counting from measuring in practical applications?

Counting yields exact numbers, while measuring can involve errors and approximations. (C) Signup and view all the answers

When is rounding most appropriate for representing numerical data?

When estimating large quantities for general understanding. (D) Signup and view all the answers

If a stadium reports attendance of 86,349 people but rounds it to the nearest thousand, what would be the rounded figure?

86,000 (A) Signup and view all the answers

What is the importance of understanding significant figures in measurements?

To reflect the precision of a measurement and avoid overstating accuracy. (D) Signup and view all the answers

A surveyor measures a plot of land to be 125.45 meters wide. What would be the measurement rounded to three significant figures?

125 m (D) Signup and view all the answers

A scientist records a measurement of 0.003857 grams. How should this number be written to two significant figures?

0.0039 (D) Signup and view all the answers

A length is recorded as 4.6 meters, measured to the nearest tenth of a meter. What are the lower and upper bounds of the actual length?

4.55 m and 4.65 m (A) Signup and view all the answers

The mass of a chemical is measured as 15.8 grams, correct to one decimal place. Within what range does the actual mass lie?

15.75 ≤ mass < 15.85 (A) Signup and view all the answers

Flashcards

Like Radicals

Radicals that have the same index and radicand.

Unlike Radicals

Radicals that have different indices or radicands.