Class 9 Math Federal Board Exercise 2.1
Class 9 Math Federal Board Exercise 2.1 solution
Q1 :- Write the following in Scientific Notation.
i) :- 0.00053407
$$=\;5.3407\;\times\;10^{-4}$$
ii) :- 53400000.
$$=\;5.34\;\times\;10^7$$
iii) :- 0.000000000012
$$=\;1.2\;\times\;10^{-11}$$
iv) :- 2.5326
$$=\;2.5326\;\times\;10^0$$
( A number is c is scientific notation if it is written as )
$$c=\;d\;\times\;10^n\\where\;n\in\mathbb{Z}\;\wedge\;1\leq d<10$$
================================
Q2 :- Write the following in standard ( ordinary ) notation.
i):-
$$\\9.067\;\times\;10^{-5\;}$$
= 0.00009067
ii):-
$$5.64\;\times\;10^{0\;}$$
= 5.64
iii):-
$$6.53\;\times\;10^{-6\;}$$
= 0.00000653
iv):-
$$3.1415\;\times\;10^9$$
= 3141500000
================================
Q3 :- Simplify the following by converting into the form indicated.
i):-
$$\;563.71\;\times\;10^{-3}\;\;\times\;2.54\;\times\;10^4\;$$
Scientific Notation
$$=\;5.637\times10^2\;\times10^{-3}\;\times\;2.54\;\times\;10^4\\=14.31798\;\times\;10^{2-3+4}$$
$$=14.31798\times\;10\;\times10^3\\=\;1.431798\;\times\;10^4$$
2nd Method
$$0.6371\times\;25400\\=\;14318.234\\=\;1.4318234\;\times10^4$$
ii):-
$$\;\frac{0.023\times10^5}{10^{-3}}\\$$
Scientific Notation
$$=\;0.023\times10^5\;\times10^3\;\\=\;0.023\;\times10^8\\=2300000.$$
iii):-
$$\;\frac{2.549\times5067\times10^{-3}}{10^3}\\\;$$
Scientific Notation
$$=\;12915.783\times10^{-3}\;\times13^{-3}\\=\;12915.783\times10^{-6}$$
$$=\;0.012915783\\=\;1.2915783\times10^{-2}$$
iv):-
$$\;\;0.0009988\times10^{10}\\$$
Scientific Notation
$$=\;9988000.\\$$
================================
Q4 :- If it takes 5 seconds to recite ‘ Kalma Pak ‘ once how many hours will it take to recite ‘ Kalma Pak ‘ one million times? Convert hours into days and write the answer in standard form. Round off the answer, discarding the decimal part.
time required to recite one time Kalma Pak
$$=\;5\;seconds$$
time required to recite one million times Kalma Pak
$$=\;5\;\times10^6\;seconds$$
$$=\;5\;\times10^6seconds\\=\;\frac{5\times10^6\;}{60}\;min$$
$$=\frac{5\times10^6\;}{60\times60}\;hours\\=\;0.0013888…\times10^6$$
$$=\;0.001389\times10^6\;\\=\;1389\;hours\\=\frac{1389}{24}\;days$$
= 57.88 days = 58 days
Another Method
$$5\times10^{6\;}\;seconds\\=\;\frac{5\times10^6}{60\times60\times24}\;days$$
$$=\;\frac{5\times10^6}{36\times1^20\times24}\;days\\=\;\frac5{864}\;\times10^6\;\times10^{-2}$$
$$=\;0.005787\times10^4\;days\\=\;57.87\;days$$
$$=\;57.9\;days\\=\;58\;days$$
================================
Q5 :-
Distance between Earth and Sun is $$9.3225600\times10^{7\;}$$ miles. If speed of light is approximately $$1.86,\;000\times10^5\;$$ miles per second, how long does it take for light to reach the Earth. Convert the answer in minutes writing in standard form.
Distance between Earth and Sun
$$=\;9.3225600\times10^{7\;}\;miles$$
Speed of light
$$=\;1.86,00\times10^{5\;}\;miles\;per\;second$$
Miles in 1 second
$$=\;1.86,00\times10^{5\;}\;$$
Time for 1 mile
$$=\;\frac1{1.86,00\times10^5}\;seconds$$
Time for
$$9.3225600\times10^{7\;}\;miles$$
$$=\frac1{1.86,00\times10^5}\times9.3225600\times10^7\;s\\=\;5.0121\times10^2\;seconds$$
$$=\;\frac{5.0121\times10^2}{60}\;min\\=0.083535\times10^2\;min\\=\;8.3535\;min$$
================================
Check! Some important links below
Video Solution 9th Class Math Exercise 2.1
Class 9 Math Federal Board Chapter 1 Notes
Home Page Notespunjab.com
