Scientific Notation Exercises

THE cientific notation is used to simply express numbers that are too small or too large.

In scientific notation, numbers are represented as follows:

$\dpi{120} \mathbf{a\cdot 10^m}$

Being The a real number, with $\dpi{120} \mathrm{1\leq \mathbf{a}<10}$ and m a integer.

See formulas for performing operations with scientific notation.

Addition:

$\dpi{120} \mathbf{a\cdot 10^{m} + b\cdot 10^{m} = (a+b)\cdot 10^{m}}$

Subtraction:

$\dpi{120} \mathbf{a\cdot 10^{m} - b\cdot 10^{m} = (a-b)\cdot 10^{m}}$

Multiplication:

$\dpi{120} \mathbf{a\cdot 10^{m} \cdot b\cdot 10^{n} = (a\cdot b)\cdot 10^{m+n}}$

Division:

$\dpi{120} \mathbf{a\cdot 10^{m}: b\cdot 10^{n} = (a: b)\cdot 10^{m-n}}$

Then check out a list of scientific notation exercises, all resolved!

Index

Scientific Notation Exercises
Resolution of question 1
Resolution of question 2
Resolution of question 3
Resolution of question 4
Resolution of question 5
Resolution of question 6
Resolution of question 7
Resolution of question 8

Scientific Notation Exercises

Question 1. Write the numbers in scientific notation:

a) 800
b) 0.08
c) 1,900,000
d) 0.0000004
e) – 11,250,000,000

Question 2. Write numbers in decimal notation:

The) $\dpi{120} 3,4\cdot 10^{-5}$

B) $\dpi{120} 7,801\cdot 10^{6}$

ç) $\dpi{120} 1.56 \cdot 10^{-9}$

d) $\dpi{120} 3.3 \cdot 10^{8}$

and) $\dpi{120} 6.7054\cdot 10^{12}$

Question 3. Calculate and write the results of additions and subtracts in scientific notation:

The) $\dpi{120} 2\cdot 10^{-4} + 7\cdot 10^{-4}$

B) $\dpi{120} 6\cdot 10^{5} + \, 2.8\cdot 10^{5}$

ç) $\dpi{120} 8.5\cdot 10^{-7} - 3.5\cdot 10^{-7}$

d) $\dpi{120} -9\cdot 10^{5} + \, 6\cdot 10^{5}$

and) $\dpi{120} 5\cdot 10^{3} + \ 4\cdot 10^{2}$

f) $\dpi{120} 8\cdot 10^{-4}+ 1\cdot 10^{-6}$

Question 4. Solve the operations and write the result in scientific notation:

a) 0.0004 + 0.035
b) 0.00008 - 0.000002
c) 0.0000250 + 0.0000009

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Question 5. Calculate and write the results of multiplications in scientific notation:

The) $\dpi{120} (7\cdot 10^{8}) \cdot (3\cdot 10^{5})$

B) $\dpi{120} (2\cdot 10^{6}) \cdot (2\cdot 10^{-6})$

ç) $\dpi{120} (2.94\cdot 10^{-4}) \cdot (1\cdot 10^{-5})$

d) $\dpi{120} (4\cdot 10^{-9})\cdot (3.6\cdot 10^{-10})$

Question 6. Calculate and write the results of divisions in scientific notation:

The) $\dpi{120} 18\cdot 10^{7}: 6\cdot 10^5$

B) $\dpi{120} 8\cdot 10^{-6}: 8\cdot 10^{4}$

ç) $\dpi{120} 3\cdot 10^{7}: 5\cdot 10^4$

d) $\dpi{120} 9\cdot 10^{8}: 3\cdot 10^{-5}$

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Question 7. The distance between the Earth and the Sun is 149,600,000 km. Express this distance in scientific notation.

Question 8. At rest, the mass of an electron corresponds to $\dpi{120} 9,10938\cdot 10^{-31}$ kg and that of a proton, the $\dpi{120} 1.672621\cdot 10^{-27}$ kg. Which of the two has the greater mass?

Resolution of question 1

The) $\dpi{120} 800 = 8\cdot 10^2$

B) $\dpi{120} 0.08 = 8\cdot 10^{-2}$

ç) $\dpi{120} 1,900,000 = 1.9\cdot 10^{6}$

d) $\dpi{120} 0.0000004 = 4\cdot 10^{-7}$

and) $\dpi{120} - 11,250,000,000 = -1,125\cdot 10^{10}$

Resolution of question 2

The) $\dpi{120} 3,4\cdot 10^{-5} =0.000034$

B) $\dpi{120} 7,801\cdot 10^{6} = 7,801,000$

ç) $\dpi{120} 1.56 \cdot 10^{-9} = 0.00000000156$

d) $\dpi{120} 3.3 \cdot 10^{8} = 330,000,000$

and) $\dpi{120} 6.7054\cdot 10^{12} = 6,705,400,000,000$

Resolution of question 3

The) $\dpi{120} 2\cdot 10^{-4} + 7\cdot 10^{-4} = (2 + 7)\cdot 10^{-4} = 9\cdot 10^{-4}$

B) $\dpi{120} 6\cdot 10^{5} + \, 2.8\cdot 10^{5} = (6 + 2.8)\cdot 10^{5}=8.8\cdot 10^{ 5}$

ç) $\dpi{120} 8.5\cdot 10^{-7} - 3.5\cdot 10^{-7} = (8.5 - 3.5)\cdot 10^{-7} = 5\cdot 10^{-7}$

d) $\dpi{120} -9\cdot 10^{5} + \, 6\cdot 10^{5} = (-9 + 6)\cdot 10^{5} = -3\cdot 10^{5}$

and) $\dpi{120} 5\cdot 10^{3} + \ 4\cdot 10^{2} = 5\cdot 10^{3} + \ 0.4\cdot 10^{3} = 5.4\cdot 10^{3}$

f) $\dpi{120} 8\cdot 10^{-4}+ 1\cdot 10^{-6} = 8\cdot 10^{-4}+ 0.01\cdot 10^{-4} = 8.01 \cdot 10^{-4}$

Resolution of question 4

The) $\dpi{120} 0.0004 + 0.035 = 0.0354 = 3.54\cdot 10^{-2}$

B) $\dpi{120} 0.000008 - 0.000002 = 0.000078 = 7.8 \cdot 10^{-5}$

ç) $\dpi{120} 0.0000250 + 0.0000009 = 0.0000259 = 2.59 \cdot 10^{-5}$

Resolution of question 5

The) $\dpi{120} (7\cdot 10^{8}) \cdot (3\cdot 10^{5}) = 7\cdot 3\cdot 10^{8+5} =21\cdot 10^{13}$

B) $\dpi{120} (2\cdot 10^{6}) \cdot (2\cdot 10^{-6}) = 2\cdot 2\cdot 10^{6-6} = 4\cdot 10^0 = 4$

ç) $\dpi{120} (2.94\cdot 10^{-4}) \cdot (1\cdot 10^{-5}) = 2.94\cdot1\cdot 10^{-4 - 5} = 2, 94\cdot 10^{-9}$

d) $\dpi{120} (4\cdot 10^{-9})\cdot (3.6\cdot 10^{-10}) = 4\cdot 3.6\cdot 10^{-9-10} = 14 ,4\cdot 10^{-19}$

Resolution of question 6

The) $\dpi{120} 18\cdot 10^{7}: 6\cdot 10^5 = (18:6)\cdot 10^{7-5} = 3\cdot 10^2$

B) $\dpi{120} 8\cdot 10^{-6}: 8\cdot 10^{4} = (8:8)\cdot 10^{-6-4} = 1\cdot 10^{-10}$

ç) $\dpi{120} 3\cdot 10^{7}: 5\cdot 10^4 = (3:5)\cdot 10^{7 - 4} = 0.6\cdot 10^{3} = 6\cdot 10^2$

d) $\dpi{120} 9\cdot 10^{8}: 3\cdot 10^{-5} = (9:3)\cdot 10^{8 -(-5)} = 3\cdot 10^{13}$

Resolution of question 7

$\dpi{120} 149,600,000 = 1,496 \cdot 10^8$

Therefore, in scientific notation, the distance between Earth and Sun is $\dpi{120} 1, 496 \cdot 10^8$ .

Resolution of question 8

To answer this question, it is enough to note that the exponent is negative in both masses. So the two quantities are less than 1, they are decimal numbers.

Therefore, the larger the exponent, the smaller the mass.

Thus, between the proton and the electron, the one with the greatest mass is the proton.

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