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<p>Two numbers, $a$ and $b$, when rounded off to the nearest $100$, are $a=200$ and $b=-100$. Given that $a$ and $b$ are integers, find</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the smallest value of $a-b$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $a+b$,</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $\frac{a}{b}$.</span><span class="inline-marks">[1]</span></div></li></ol>

Two numbers, $a$ and $b$, when rounded off to the nearest $100$, are $a=200$ and $b=-100$. Given that $a$ and $b$ are integers, find

IP1 Class Test (May 2025) Q8

Approximation and Estimation

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

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

IP1 Class Test (May 2025) Q7

<p>Given that $\sqrt{5.23} = 2.287$ and $\sqrt{52.3} = 7.232$, without using a calculator, evaluate</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">$\sqrt{523}$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\sqrt{52300}$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">$\sqrt{0.0523}$.</span></div></li></ol>

Given that $\sqrt{5.23} = 2.287$ and $\sqrt{52.3} = 7.232$, without using a calculator, evaluate

Approximation and Estimation - General

<p>Two numbers, when rounded off to the nearest 100, are $a = 1500$ and $b = 2800$. Given that $a$ and $b$ are integers, find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the largest value of $a - b$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest value of $a + b$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest value of $a \times b$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $a \times b$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the smallest value of $\frac{a}{b}$,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the largest value of $\frac{a}{b}$.</span></div></li></ol>

Two numbers, when rounded off to the nearest 100, are $a = 1500$ and $b = 2800$. Given that $a$ and $b$ are integers, find

<p>A vehicle travels $148$ km. On average, it travels $10.3$ km for every litre of petrol.</p>
<p>Write down an expression that mentally estimates the amount of petrol used.</p>

A vehicle travels $148$ km. On average, it travels $10.3$ km for every litre of petrol.

Write down an expression that mentally estimates the amount of petrol used.

Estimation

<p>The mass of a strawberry is $0.019$ g, correct to $2$ significant figures. What is the smallest possible mass of the strawberry?</p>

The mass of a strawberry is $0.019$ g, correct to $2$ significant figures. What is the smallest possible mass of the strawberry?

Significant Figures

<p>Given that $20.63^2 = 425.6$, without the use of calculator, find $0.02063^2$.</p>

Given that $20.63^2 = 425.6$, without the use of calculator, find $0.02063^2$.

<p>Given that $2.853^3 = 23.22$, without the use of calculator, find $28.53^3$.</p>

Given that $2.853^3 = 23.22$, without the use of calculator, find $28.53^3$.

<p>Given that $6.352^2 = 40.35$, without the use of calculator, find $63.52^2$.</p>

Given that $6.352^2 = 40.35$, without the use of calculator, find $63.52^2$.

<p>A number when it is rounded off to $3$ significant figures is $450\ 000$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the largest possible integer of the number.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the smallest possible value of the number.</span></div></li></ol>

A number when it is rounded off to $3$ significant figures is $450\ 000$.

Find the largest possible integer of the number.

Find the smallest possible value of the number.

<p>A number when it is rounded off to $2$ significant figures is $8100$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the largest possible integer of the number.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the smallest possible value of the number.</span></div></li></ol>

A number when it is rounded off to $2$ significant figures is $8100$.

<p>A number when it is rounded off to $3$ significant figures is $253\ 000$.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the largest possible integer of the number.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the smallest possible value of the number.</span></div></li></ol>

A number when it is rounded off to $3$ significant figures is $253\ 000$.

<ol class="abc-list"><li><div class="list-item-paragraph">Without the use of calculator, estimate the value of $\frac{10.97 \times 7.89}{21.97}$ correct to $1$ significant figure.</div></li><li><div class="list-item-paragraph">Using your result in (a), estimate the value of $\frac{0.1097 \times 78.9}{219.7}$ correct to $1$ significant figure.</div></li></ol>

Without the use of calculator, estimate the value of $\frac{10.97 \times 7.89}{21.97}$ correct to 1 significant figure.

Using your result in (a), estimate the value of $\frac{0.1097 \times 78.9}{219.7}$ correct to 1 significant figure.

Significant Figures and Estimation

<p>The circumference of a circle is $15$ cm. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the radius,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the area,</span></div></li></ol>
<p>of the circle, leaving your answers in $4$ significant figures.</p>

The circumference of a circle is $15$ cm. Find

of the circle, leaving your answers in $4$ significant figures.

<p>The area of a square is $89$ m$^2$. Find</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">the length of a side,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the perimeter of the square,</span></div></li></ol>
<p>giving each of your answers correct to $4$ significant figures.</p>

giving each of your answers correct to $4$ significant figures.

<p>A bicycle costs $380$ Malaysian Ringgit.</p>
<p>The conversion rate at the time of purchase was $1$ Singapore Dollar = $3.2694$ Malaysian Ringgit.</p>
<p>Without using a calculator, estimate the price of the bicycle in Singapore Dollars.</p>

The conversion rate at the time of purchase was $1$ Singapore Dollar = $3.2694$ Malaysian Ringgit.

Without using a calculator, estimate the price of the bicycle in Singapore Dollars.

<p>A camera costs $127\ 500$ Japanese Yen.</p>
<p>The conversion rate at the time of purchase was $1$ Singapore Dollar = $99.7$ Japanese Yen.</p>
<p>Without using a calculator, estimate the price of the camera in Singapore Dollars.</p>

The conversion rate at the time of purchase was $1$ Singapore Dollar = $99.7$ Japanese Yen.

Without using a calculator, estimate the price of the camera in Singapore Dollars.

<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>

$0.000\ 599\ 81$ to 3 significant figures,

$0.000\ 027\ 37$ to 2 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>

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