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<ol class="i-list"><li data-list-item-id="item-i" data-list-item-path="item-i"><div class="list-item-paragraph">Express $10893.69775$ to</div><ol class="abc-list"><li data-list-item-id="item-i-a" data-list-item-path="item-i/item-i-a"><div class="list-item-paragraph">$3$ significant figures,<span class="inline-marks">[1]</span></div></li><li data-list-item-id="item-i-b" data-list-item-path="item-i/item-i-b"><div class="list-item-paragraph">the nearest hundredth.<span class="inline-marks">[1]</span></div></li></ol></li><li data-list-item-id="item-ii" data-list-item-path="item-ii"><div class="list-item-paragraph">Given that&nbsp;$\sqrt{7.89}\approx 2.809$, $\sqrt[3]{7.89}\approx 1.991$ and $\sqrt{78.9}\approx 8.883$, showing your working clearly, evaluate,</div><ol class="abc-list"><li data-list-item-id="item-ii-a" data-list-item-path="item-ii/item-ii-a"><div class="list-item-paragraph">$\sqrt{789000}$,<span class="inline-marks">[2]</span></div></li><li data-list-item-id="item-ii-b" data-list-item-path="item-ii/item-ii-b"><div class="list-item-paragraph">$\sqrt[3]{0.00789}$,<span class="inline-marks">[2]</span></div></li></ol></li></ol>

Given that $\sqrt{7.89}\approx 2.809$, $\sqrt[3]{7.89}\approx 1.991$ and $\sqrt{78.9}\approx 8.883$, showing your working clearly, evaluate,

Rounding Off

Scaling Given Approximations

Significant Figures

IP1 Class Test (May 2025) Q7

Approximation and Estimation

<p>Correct</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$0.000\ 599\ 81$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$0.000\ 027\ 37$ to $2$ significant figures,</div></li><li><div class="list-item-paragraph">$0.0078012$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$0.100545$ to $4$ significant figures.</div></li></ol>

 Significant Figures

<p>Correct</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$57\ 344$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$344\ 876$ to $4$ significant figures,</div></li><li><div class="list-item-paragraph">$1.0022$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$73.0951$ to $4$ significant figures.</div></li></ol>

<p>Correct</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$36\ 285$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$54\ 846$ to $4$ significant figures,</div></li><li><div class="list-item-paragraph">$73.15$ to $3$ significant figures,</div></li><li><div class="list-item-paragraph">$8.1005$ to $4$ significant figures.</div></li></ol>

<ol class="i-list"><li><div class="list-item-paragraph">The mass of the Sun is $1.99\times {{10}^{27}}$ tonnes.
</div><div class="list-item-paragraph">Write this mass, in kilograms, giving your answer in standard form. ($1$ tonne $=1000$kg)</div></li><li><div class="list-item-paragraph">The radius of a micro-organism is $0.000\,054\,65$cm.
</div><div class="list-item-paragraph">Express $0.000\,054\,65$cm in standard form, giving your answer correct to $3$ significant figures.</div></li></ol>

Standard Form

Converting Metric Prefixes Using Powers of Ten

Standard Form in Measurement Problems

Standard Form and Compound Interest

<p>Express each of the following, rounded off to the required number of significant figures stated in brackets with the use of a calculator.</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--3" data-layout="3"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li data-list-item-id="item-1792396083925-18eejoz1c" data-list-item-path="item-1792396083925-18eejoz1c"><div class="list-item-paragraph"><p>$\sqrt{19.5^{2}+\frac{36.4^{2}}{8.2}}$ (3 s.f.)</p></div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list" start="2"><li data-list-item-id="item-1792396103109-ew6m2k8jw" data-list-item-path="item-1792396103109-ew6m2k8jw"><div class="list-item-paragraph"><p>$\frac{5.24}{\sqrt{21.5\times 0.569}}$ (2 s.f.)</p></div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list" start="3"><li data-list-item-id="item-1792396124655-avh5la08f" data-list-item-path="item-1792396124655-avh5la08f"><div class="list-item-paragraph"><p>$\sqrt[3]{\frac{3.123^{2}-\pi}{52.17\times 86.42}}$ (4 s.f.)</p></div></li></ol></div></div></div>

Express each of the following, rounded off to the required number of significant figures stated in brackets with the use of a calculator.

Rounding Off to a Required Number of Significant Figures with Use of a Calculator

<p>Express each of the following, rounded off to the required number of significant figures stated in brackets.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$2345.678$ (3 s.f.)</div></li><li><div class="list-item-paragraph">$0.09127$ (2 s.f.)</div></li><li><div class="list-item-paragraph">$82180.15$ (3 s.f.)</div></li><li><div class="list-item-paragraph">$0.00473$ (4 s.f.)</div></li></ol>

Express each of the following, rounded off to the required number of significant figures stated in brackets.

Rounding off to a Required Number of Significant Figures

<ol class="abc-list"><li><div class="list-item-paragraph">Calculate $\frac{{{154}^{2}}}{\sqrt[3]{135}-2.67}$, giving your answer correct to 3 significant figures.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">The mass of a cone is $25.0$ g, rounded off to the nearest 1 decimal place.</div><div class="list-item-paragraph">Write down the minimum mass of the cone.</div><p style="text-align: right;">[1]</p></li></ol>

Error Bounds and Percentage Error

2023 AISS S3 EM P1 Q1

<ol class="abc-list"><li><div class="list-item-paragraph">Round off the number ${20725}$ to $3$ significant figures.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Calculate $\frac{-{{0.123}^{3}}}{\sqrt[3]{52}-3.9}$. Write your answer correct to $2$ decimal places.</div><p style="text-align: right;">[1]</p></li></ol>

2023 AISS EM S1 EOY P1 Q2

<ol class="abc-list"><li><div class="list-item-paragraph">Calculate ${\frac{12.3^2}{\sqrt[3]{4} - 5}}$. Write down the first four digits of your answer.</div><p style="text-align: right;">[1]</p></li><li><div class="list-item-paragraph">Write down your answer to part <strong>(a)</strong> correct to ${2}$ significant figures.</div><p style="text-align: right;">[1]</p></li></ol>

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