More on Absolute Values

Your true weight is $100$ pounds, but a scale says you weigh $105$ pounds. Find the relative error.

Define true value of measurement. The true value is $252.14$ mm and the measured value is $249.02$ mm. Find the absolute error.

Define true value of measurement. The true value is $125.68$ mm and the measured value is $119.66$ mm. Find the absolute error.

Scientists announced the discovery of a potential "Planet Nine" in our solar system in $2016.$

The so-called "Planet Nine" is about $5000$ times the mass of Pluto. Pluto's mass is $0.01303\times {10}^{24} \mathrm{kg}$.

The Earth's mass is $5.97\times {10}^{24} \mathrm{kg}$. Find how many times Planet Nine is bigger or smaller compared to the Earth. Write down your answer correct to the nearest digit.

Scientists announced the discovery of a potential "Planet Nine" in our solar system in $2016.$

The so-called "Planet Nine" is about $5000$ times the mass of Pluto. Pluto's mass is $0.01303\times {10}^{24} \mathrm{kg}$.

Calculate the mass of Planet Nine. Write down your answer in standard form.

Convert the following from scientific to decimal notation: $5\times {10}^3$.

Convert the following from decimal to scientific notation:

Age of the Earth $=4600000000$ years.

The image of a speck of dust viewed through an electron microscope is $1.2\times {10}^2$ millimetres wide. The image is $5\times {10}^2$ times as large as the actual size. Determine the width, in millimetres, of the actual speck of dust.

Write down the following number found on a calculator display in scientific notation:

$\mathrm{1E}-3$

Write down the following number found on a calculator display in scientific notation:

$4.005\mathrm{E}-7$

Write down the following number found on a calculator display in scientific notation:

$5.04\mathrm{E7}$

Write down the following number found on a calculator display in scientific notation:

$1.2\mathrm{E}-1$

Find the measurement below in the form of $a\times {10}^n\text{ , where }1\le a<10$ and $n$ is an integer.

The mass of a neutron, $0.000000000000000000000001675 \mathrm{g}$

Find the measurement below in the form of $a\times {10}^n\text{ , where }1\le a<10$ and $n$ is an integer.

One light year, $9460000000000 \mathrm{km}$

Find the measurement below in the form of $a\times {10}^n\text{ , where }1\le a<10$ and $n$ is an integer.

The radius of calcium atom, $0.000000000197 \mathrm{m}$

Find the measurement below in the form of $a\times {10}^n\text{ , where }1\le a<10$ and $n$ is an integer.

Density of air at $27° C$ and $1 \mathrm{atm}$ pressure, $0.00161 \mathrm{g}/{\mathrm{cm}}^3$

In an experiment time period of a simple pendulum are measured as $2.63 \mathrm{s},2.56 \mathrm{s}$, $2.71 \mathrm{s},2.80 \mathrm{s}$. Find average absolute error and the percentage error.

Students $A,B$ and $\mathrm{C}$ measure the length of a room using $25 \mathrm{m}$ long measuring tape of least count $\mathrm{LC}$ $0.5 \mathrm{cm},$ meter-scale of $\mathrm{LC} 0.1 \mathrm{cm}$ and a foot-scale of $\mathrm{LC} 0.05 \mathrm{cm},$ respectively. If the specified length of the room is $9.5 \mathrm{m},$ then which of the following students will report the lowest relative error in the measured length? $\left(1 \mathrm{foot}=30.48 \mathrm{cm}\right)$

What are errors?