Question
Work out, giving each answer in standard form.
$( \mathbf{a} )$ $\left ( 2. 1\times 10^{101}\right ) \times \left ( 8\times 10^{101}\right )$
$( \mathbf{b} )$ $\left ( 2. 1\times 10^{101}\right ) + \left ( 2. 1\times 10^{100}\right )$
▶️Answer/Explanation
(a) $1.68 \times 10^{203}$
(b) $2.31 \times 10^{101}$
(a)
$
(2.1 \times 10^{101}) \times (8 \times 10^{101})
$
coefficients
$
2.1 \times 8 = 16.8
$
exponents (laws of indices):
$
10^{101} \times 10^{101} = 10^{202}
$
$
= 16.8 \times 10^{202}
$
$
= 1.68 \times 10^{203}
$
(b)
$
(2.1 \times 10^{101}) + (2.1 \times 10^{100})
$
common coefficient
$
= 2.1 \times 10^{100}(10^1 + 1)
$
$
= 2.1 \times 10^{100}(10 + 1)
$
$
= 2.1 \times 10^{100} \times 11
$
$
= 23.1 \times 10^{100}
$
$
= 2.31 \times 10^{101}
$
Question
Write $174000$ in standard form.
▶️Answer/Explanation
$1.74\times 10^5$
Standard form is written as
$
a \times 10^n \quad \text{where} \, 1 \leq a < 10
$
$
174000 = 1.74 \times 10^5
$
Question
Without using your calculator, work out \(1\frac{5}{6}+\frac{9}{10}.\)
You must show your working and give your answer as a mixed number in its simplest form.
Answer/Explanation
Ans: \(\frac{55}{30}+\frac{27}{30}oe or (1)\frac{25}{30}+\frac{27}{30}oe\frac{82}{30}oe or(1)\frac{52}{30}oe2\frac{11}{15}\) M2 must be scored
Question
Write as a single fraction in its simplest form.
\(3 – \frac{t+2}{t-1}\)
Answer/Explanation
Ans:
\(\frac{2t-5}{t-1}\) final answer
Question
Give each answer as a fraction in its lowest terms.
Work out.
(a) \(\frac{3}{4} – \frac{1}{12}\)
(b) \(2 \frac{1}{2} \times \frac{4}{25}\)
Answer/Explanation
Ans:
(a) \(\frac{9}{12} – \frac{1}{12}\) oe
\([=]\frac{8}{12}\) oe \([=] \frac{2}{3}\)
(b) \(\frac{5}{2} \times \frac{4}{25}\) oe
Cancelling shown or \(\frac{21}{50}\) oe \([=]\frac{2}{5}\)