Question
Find the value of the reciprocal of $0.4$ .
▶️Answer/Explanation
2.5 oe
$
\text{Reciprocal of } 0.4 = \frac{1}{0.4}
$
convert 0.4 to a fraction
$
0.4 = \frac{4}{10} = \frac{2}{5}
$
the reciprocal of the fraction
$
\frac{1}{\frac{2}{5}} = \frac{5}{2}
$
$
\frac{5}{2} = 2.5
$
Question
(a) Work out.
\(28-16\div 2\)
(b) Find the reciprocal of \(\frac{4}{5}\).
▶️Answer/Explanation
Ans:
(a) 20
(b) 1.25 or \(1\frac{1}{4}\)
(a)
Follow the order of operations (BIDMAS/BODMAS):
Division comes before subtraction
$16 \div 2 = 8$
$28 – 8 = 20$
(b)
The reciprocal of a fraction means flipping it (swap the numerator and denominator):
$\text{Reciprocal of } \frac{4}{5} = \frac{5}{4}$
Question
Find the value of
(a) \(9^4\),
(b) \(6^0\)
▶️Answer/Explanation
(a) \(9^{4}=4\times 4\times 4\times 4=6561\)
(b) Any non-zero number raised to the power of zero is equal to 1. Therefore, \(6^{0}=1\)
Question
(a) Calculate \(\sqrt{5.7} – 1.03^2\).
Write down all the numbers displayed on your calculator.
(b) Write your answer to part (a) correct to 3 decimal places.
▶️Answer/Explanation
(a) Using a calculator, we get \(\sqrt{5.7} – 1.03^2= 2.387467277 – 1.0609= 1.326567277\)
(b) Rounding the answer to 3 decimal places ,we get \(\sqrt{5.7} – 1.03^2\approx 1.327\)
Question
By writing each number correct to 1 significant figure, estimate the value of \(\frac{\sqrt{3.9}\times 29.3}{8.9-2.7}.\)
Show all your working.
▶️Answer/Explanation
Here,we have to round of each number to 1 significant figure.So,
significant figure for 3.9 is 4
significant figure for 29.3 is 29
significant figure for 8.9 is 9
significant figure for 2.7 is 3
\(\frac{\sqrt{4}\times 29}{9-3}\)=\(9.66\approx 10\)
Question
Calculate.
\(3.2\times \left ( 5.7-1.3 \right )+4.8\)
▶️Answer/Explanation
We can evaluate the expression by using order of operations (PEMDAS) as follows,
First, we evaluate the expression inside the parentheses
5.7−1.3=4.4
Now, we multiply \(3.2\times 4.4=14.08\)
Finally, we add 14.08+4.8=18.88
Therefore,
\(3.2\times \left ( 5.7-1.3 \right )+4.8=18.88\)
(b) \(\sqrt{2.54-0.85}\)
▶️Answer/Explanation
We can start by evaluating the expression inside the square root 2.54-0.85=1.69
So now we have
\(\sqrt{2.54-0.85}=\sqrt{1.69}=1.3\)
Therefore, the answer is 1.3
Question
(a) Find the value of $p$ when $p^3=-27$.
(b) Find the value of $q$ when $q^{-1}=\frac{1}{6}$.
(c) Simplify $8 s^2 \div 2 s^{-1}$.
▶️Answer/Explanation
(a) -3 final answer
(b) 6 final answer
(c) $4 s^3$ or $\frac{4}{s^{-3}}$ final answer