Subject: Compulsory Maths

Scientific notation is, essentially, a method for writing really big or really small numbers. It is called scientific notation because these huge numbers are often found in scientific work. For example, you might have the number 6000000000000. That’s really big, right? Unfortunately, it isn’t easy to tell exactly how big at first glance with all those zeroes stuck on the end. Instead, the number could be written as 6 * 1000000000000. Then you can change it.

Scientific Notation is used to handle very large or very small numbers. Scientists have developed a shorter method to express very large numbers. It is written as the product of a number (integer and decimal) and a power of 10.

Here are some examples of scientific notation.

10,000 = 1\(\times\)10^{4} |
34,567 = 3.4567\(\times\) 10^{4} |

1000 = 1\(\times\)10^{3} |
495 = 4.95 \(\times\)10^{2} |

10 = 1\(\times\)10^{1} |
98 = 9.8 \(\times\)10^{1}(not usually done) |

\(\frac{1}{10}\)=1\(\times\)10^{-1} |
0.23 = 2.3 \(\times\)10^{-1}(not usually done) |

\(\frac{1}{100}\)= 1\(\times\)10^{-2} |
0.026 = 2.6\(\times\)10^{-2} |

\(\frac{1}{1000}\) = 1\(\times\)10^{-3} |
0.0064 =6.4\(\times\)10^{-3} |

\(\frac{1}{10,000}\) = 1\(\times\)10^{-4} |
0.00088 = 8.8\(\times\)10^{-4} |

**Example:**

0.000457

= \(\frac{0.000457\times 1000000}{1000000}\)

=\(\frac{457}{10^6}\)

=457\(\times\) 10^{-6}

=4.57\(\times\)10^{2}\(\times\)10^{-6}

= 4.57\(\times\)10^{-4}

- Scientific notation is the way that scientists easily handle very large numbers or very small numbers.
- Scientific notation can be used to turn 0.0000053 into 5.3 x 10
^{-6} - A power of ten with a positive exponent, such as 10
^{5}, means the decimal was moved to the left. - A power of ten with a negative exponent, such as 10
^{-5}, means decimal was moved to the right.

- It includes every relationship which established among the people.
- There can be more than one community in a society. Community smaller than society.
- It is a network of social relationships which cannot see or touched.
- common interests and common objectives are not necessary for society.

Write down in scientific notation.

324000000

Solution:

324000000

= 324 × 10^{6}

= 3.24 × 10^{2}× 10^{6}

= 3.24 × 10^{2+6}

= 3.24 × 10^{8}

Write down in scientific notation.

45000000

Solution:

45000000

= 45×10^{6}

= 4.5×10^{1}×10^{6}

= 4.5×10^{1+6}

= 4.5×10^{7}

Write down in scientific notation.

45

Solution:

45

= 4.5×10

= 4.5×10^{1}

Write down in scientific notation.

101000

Solution:

101000

=1.01×100000

=1.01×10^{5}

Write down in scientific notation.

0.00671

Solution:

0.00671

= \(\frac{6.71}{100000}\)

= \(\frac{6.71×100}{10^5}\)

= 6.71×10^{2-5}

=6.71×10^{-3}

Express the following in scientific notation.

0.0000435

Solution:

0.0000435

= \(\frac{0.0000435×10000000}{10000000}\)

= \(\frac{435}{10^7}\)

Express in scientific notation.

0.0000435

Solution:

0.0000435

= \(\frac{0.0000435×10000000}{10000000}\)

= \(\frac{435}{10^7}\)

Convert in general form:

2.4×10^{5}

Solution:

= 2.4×10^{5}

= 240000

Convert in general form

5.7 × 10^{1}×10^{-4-1}

Solution:

5.7× 10^{1}×^{-4-1}

= 57× 10^{-4-1}

= 57× 10^{-5}

= \(\frac{57}{10^5}\)

= \(\frac{57}{100000}\)

= 0.00057

Simplify and give your answers in scientific notation:

3.2 ×10^{4}+2.3 ×10^{4}

Solution:

= 3.2×10^{4}+2.3×10^{4}

= (3.2+2.3)×10^{4}

= 5.5×10^{4}

Simplify and give answer in scientific notation:

2.6×10^{3}+3.4×100

Solution:

2.6×1000 + 3.4×100

=2600 +340

= 2940

= 294×10^{1}

= 2.94×10^{2}×10^{1}

= 2.94× 10^{3}

Simplify and give answer in scientific notation:

8.3×10^{2 }- 2.4×10^{2}

Solution:

8.3×100 - 2.4×100

= 830-240

= 590

= 59×10^{1}

= 5.9×10^{2}

The mass of the moon is 72,000,000,000,000,000,000,000 kg. What is this written in scientific notation.

Solution:

72,000,000,000,000,000,000,000 kg.

= 72 × 10^{18}kg

= 7.2×10^{1}×10^{18} kg

= 7.2×10^{19} kg

The speed of the light in a vacuum is 299792458 m/s. What is this written in scientific notation.

Solution:

299792458

= 2.99792458 × 100000000

= 2.99792458 × 10^{8} m/s

Write down in Scientific notation.

3.2 × 10^{4} + 2.3 × 10^{4}

Solution:

3.2 × 10^{4} + 2.3 × 10^{4}

= ( 3.2 + 2.3 )× 10^{4}

= 5.5× 10^{4}

Simplify in scientific notation.

9.70 × 10^{6} + 8.3 × 10^{5}

Solution:

9.70 × 10^{6} + 8.3× 10^{5}

= 9.70× 10^{6} + 0.83× 10^{6}

= (9.70 + 0.83)× 10^{6}

= 10.53×10^{6}

= \(\frac{10.53}{10}\)× 10× 10^{6}

= 1.053×10^{1+6}

= 1.053×10^{7}

Simplify and give the answer in Scientific notation.

(1.2 × 10^{5}) + ( 5.35 × 10^{6})

Solution:

1.2× 10^{5}

= \(\frac{1.2}{10}\) × 10× 10^{5}

= 0.12× 10^{6}

Now,

( 1.2× 10^{5}) + (5.35× 10^{6} )

= ( 0.12× 10^{6}) + (5.35× 10^{6})

= (0.12 + 5.35)× 10^{6}

= 5.47× 10^{6}

Simplify and give the answer in Scientific notation.

8.41 × 10^{-5} - 7.00 × 10^{-6}

Solution:

7.00× 10^{-6}

= \(\frac{7.00}{10}\)× 10^{1}×10^{-6}

= 0.70× 10^{1-6}

= 0.70× 10^{-5}

Now,

8.41× 10^{-5} - 0.70× 10^{-5}

= 8.41× 10^{-5} - 0.70× 10^{-5}

= (8.41 - 0.70)× 10^{-5}

= 7.71× 10^{-5}

Simplify and give answers in Scientific notation.

\(\frac{1.20 × 10^{-8}}{3.0 ×10^{-3}}\)

Solution:

\(\frac{1.20× 10^{-8}}{3.0×10^{-3}}\)

= \(\frac{1.20}{3}\)\(\times\)10^{-8 + 3}

= 0.40\(\times\)10^{-5}

= \(\frac{40}{100}\)\(\times\) 10^{-5}

= \(\frac {4.0 \times 10^1 \times 10^{-5}}{10^2}\)

=\(\frac{4.0\times10^{1-5}}{10^2}\)

= 4.0 \(\times\)10^{-4-2}

= 4.0\(\times\)10^{-6}

Simplify and give answers in Scientific notation:

6.91 × 10^{-2} + 2.4 × 10^{-3}

Solution:

2.4× 10^{-3}

= \(\frac{2.4}{10}\)× 10× 10^{-3} = 0.24× 10^{-2}

Now,

6.91× 10^{-2} + 0.24× 10^{-3}

= 6.91× 10^{-2} + 0.24× 10^{-2}

=(6.91 + 0.24 )× 10^{-2}

= 7.15× 10^{-2}

Simplify and give your answer in Scientific Notation.

1.33\(\times\)10^{5} - 4.9 \(\times\)10^{4}.

Solution:

4.9 \(\times\)10^{4}

= \(\frac{4.9}{10}\)\(\times\)10^{1}\(\times\)10^{4}

= 0.49 \(\times\)10^{1+4}

= 0.49\(\times\)10^{5}

Now,

1.33\(\times\)10^{5} - 4.9 \(\times\)10^{4}

= 1.33 \(\times\)10^{5} - 0.49\(\times\)10^{5}

= (1.33 - 0.49) \(\times\)10^{5}

= 0.84 \(\times\)10^{5}

= \(\frac{8.4}{10}\)\(\times\)10^{5}

= 8.4\(\times\)10^{4}

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