- Convert 0.2 into a fraction.
- \(\tfrac{1}{5}\)
- \(\tfrac{11}{50}\)
- \(\tfrac{2}{9}\)
- \(\tfrac{2}{7}\)
To convert a terminating decimal to a fraction, write 0.2 as \(\tfrac{2}{10}\), then simplify by dividing numerator and denominator by 2:
\(\tfrac{2}{10} = \tfrac{1}{5}\)
- What is the decimal expansion of \(\tfrac{5}{6}\)?
- 0.(56)
- 0.83
- 0.56
- 1.2
Dividing \(\tfrac{5}{6}\) gives \(0.8333\ldots\), so the closest match among the choices is 0.83.
- Which number is the closest approximation to \(\tfrac{\pi}{4}\)?
- 0.85
- 1.0
- 0.785
- 1.273
Since \(\pi\approx3.1416\), dividing by 4 gives \(\tfrac{\pi}{4}\approx0.7854\), and 0.785 is the closest choice.
- Without using a calculator, identify which point on the number line could be \(\sqrt{3}\)?
- Point A
- Point B
- Point C
- Point D
Because \(1^2=1 \lt 3 \lt 4=2^2\), it follows that \(1 \lt \sqrt{3} \lt 2\). On the number line, only point C lies between 1 and 2.
- Simplify \(5^2 \times 5^4 \times 5^{-4} \times 5^{-2}\).
- 1
- 5
- 0
- 2.5
Adding the exponents gives \(2 + 4 + (-4) + (-2) = 0\), so the product is \(5^0 = 1\).
- Simplify \(\bigl(\tfrac{2}{3}\bigr)^{-3}\).
- \(\tfrac{8}{27}\)
- \(\tfrac{27}{8}\)
- \(\tfrac{-8}{27}\)
- \(\tfrac{-27}{8}\)
A negative exponent takes the reciprocal.
\(\bigl(\tfrac{2}{3}\bigr)^{-3} = \bigl(\tfrac{3}{2}\bigr)^{3} = \tfrac{27}{8}\)
- Solve the equation for x: \(x^2 = 16\).
- \(x = 4\)
- \(x = ±4\)
- \(x = 8\)
- \(x = ±8\)
Taking the square root of both sides gives \(x = \pm\sqrt{16} = \pm4\), since an even root yields both positive and negative solutions.
- Solve the equation for \(x\):
- \(x = -9\)
- \(x = ±9\)
- \(x = -3\)
- \(x = ±3\)
Taking the cube root of both sides gives \(x = \sqrt[3]{-27} = -3\). For odd roots, there is a single real solution that carries the sign of the radicand.
- What is the decimal notation of \(7\times10^{-4}\)?
- 70,000
- 7,000
- 0.00007
- 0.0007
Multiplying by \(10^{-4}\) moves the decimal point four places to the left.
\(7\times10^{-4} = 0.0007\)
- What is 0.0143 written in scientific notation?
- \(1.43\times10\)
- \(1.43\times10^{2}\)
- \(1.43\times10^{-1}\)
- \(1.43\times10^{-2}\)
A number in scientific notation has the form \(a\times10^n\) with \(1\le a \lt 10\). Writing \(0.0143\) as \(1.43\times10^{-2}\) moves the decimal two places right and multiplies by \(10^{-2}\).