Question

The actual length of a painting was 2m .What is its length in the photograph, if the scale used is 1mm: 20cm.

Answer 1

Hint: To find the length of the painting in the photograph first convert the 2m in terms of centimeter and try to relate the length using the scale given in the question which is 1mm: 20cm.
That is, convert the quantity 2m in terms of cm than in terms of mm (using the given scale).

Formula Used:
Here we will use the relation between the metric prefixes.
That is,
1m=100cm
For converting cm into mm we will use the reference scale which is given in the question that is 1mm: 20cm.

Complete step-by-step answer:
In the question it is given that the actual size of painting was 2m.
The scale of the photograph is also given
That is,
 1mm=2cm
We will take this scale as our reference to find out the length of painting in the photograph.
We know that,
1m= 100 cm
$\Rightarrow $ 2m= 200cm
Now,
 According to the given scale,
2cm= 1mm,
 $\Rightarrow $ 1cm = (1/2)mm
$\Rightarrow $1cm= 0.5mm
$\Rightarrow $200cm= 200 $\times $ 0.5 mm
$\Rightarrow $200cm= 100mm {200 $\times $ 0.5= 100.0}
$\Rightarrow $ 2m=200 cm = 100mm
$\Rightarrow $the length of the painting in the photograph according to the given scale (2cm= 1mm) is equal to 100mm.

Additional Information:

	Symbol	Factor
Tera	T	${{10}^{12}}$
Giga	G	${{10}^{9}}$
Mega	M	${{10}^{6}}$
Kilo	K	${{10}^{3}}$
Hecto	h	${{10}^{2}}$
Deca	da	${{10}^{1}}$
Deci	d	${{10}^{-1}}$
Centi	c	${{10}^{-2}}$
Milli	m	${{10}^{-3}}$
Micro	µ	${{10}^{-6}}$
Nano	n	${{10}^{-9}}$
Pico	p	${{10}^{-12}}$

Note: The knowledge of the metric prefixes and their symbols is important for students to solve this question. Their relation with each other is also required to answer this question.