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Formative: Rational Numbers, Exponents and Standard Form

Last updated 10 months ago

7 Nsɛmmisa

Simple and Familiar (1 - 2)

1

1

Complex and Familiar (3 - 4)

1

1

Challenging and Familiar (5 - 6)

1

1

Challenging and Unfamilar (7 - 8)

1

Asemmisa {{asɛmmisaAhyɛnsode}}

1.

Without using the calculator, simplify the following expressions. It is not necessary to show your work here.
$2^{2}+2^{3}$
$2^{2}\times2^{3}$
$(-5)^{-1}\times(-5)^{6}$
$\frac{7^{0}}{7^{-4}}$

Asemmisa {{asɛmmisaAhyɛnsode}}

2.

Convert to Scientific Notation, no work needed.
$0.000045209$
$230084000000$

Asemmisa {{asɛmmisaAhyɛnsode}}

3.

Convert the following recurring decimals to fractions. Show your work.
$0.333...$
$1.21212...$

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4.

Evaluate the following expression, give your answer as a simplified fraction without exponents. Show your work.
$\frac{6^{5}}{6^{2}} \times \frac{9^{-1}}{9^{1}}$

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5.

$\text{5. Which of the following is equal to } x \text{? Explain your choice.}$

$x^{\tfrac{12}{7}} - x^{\tfrac{5}{7}}$

$\sqrt[12]{\left(x^{4}\right)^{\tfrac{1}{3}}}$

$\left(\sqrt{x^{3}}\right)^{\tfrac{2}{3}}$

$x^{\tfrac{12}{7}} \times x^{\tfrac{7}{12}}$

Asemmisa {{asɛmmisaAhyɛnsode}}

6.

Simplify the following expressions and write the answer in positive exponents only.
$\left( \frac{10x^{2}y^{-2}z^{2}}{(3x^{5}y^{3}z^{-1})^{-1}} \right)^{2} \left(\frac{-xy}{30z}\right)$

Asemmisa {{asɛmmisaAhyɛnsode}}

7.

In chemistry, the unit of mass used to study atoms is called a unified atomic mass unit (u).
$1u = \frac{1}{12} \times \text{(mass of a carbon-12 atom)}$and is approximately,
$1u \approx 1.6605 \times 10^{-27} \, \text{kg}$
Find the mass, in g, of a carbon-12 atom.
Find the mass, in g, of a hydrogen-1 atom (a hydrogen-1 atom has a mass of $1.0078 u$)
An oxygen atom has a $\text{Mass of } 15.999u$. Find the mass, in g, of a water molecule ($\text{Mass of water molecule} = 2 \times (1.0078u) + 15.999u .$