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JulijaS [17]
3 years ago
9

Express the following in regular notation: 3.4 x 10-1

Chemistry
2 answers:
sweet-ann [11.9K]3 years ago
3 0

Answer:

hen working with very large or very small numbers, scientists, mathematicians, and engineers often use scientific notation to express those quantities. Scientific notation uses exponential notation. The following are examples of scientific notation.

Light year: number of miles light travels in one year, about 5,880,000,000,000

           Scientific notation is 5.88 x 1012 miles.

hydrogen atom: has a diameter of about 0.00000005 mm

Scientific notation is 5 x 10-8 mm

Computation with very large numbers is made easier with scientific notation.

Learning to Use Scientific Notation

When a number is written in scientific notation, the exponent tells you if the term is a large or a small number. A positive exponent indicates a large number and a negative exponent indicates a small number that is between 0 and 1.

Since it’s so useful, let’s look more closely at the details of scientific notation format.

Scientific Notation

A positive number is written in scientific notation if it is written as a x 10n where the coefficient a has a value such that 1 ≤ a < 10 and n is an integer.

Look at the numbers below. Which of the numbers is written in scientific notation?

Number

Scientific Notation?

Explanation

1.85 x 10-2

yes

1 ≤1.85 < 10

-2 is an integer

no

is not an integer

0.82 x 1014

no

0.82 is not ≥ 1

10 x 103

no

10 is not < 10

Which number below is written in scientific notation?

A) 4.25 x 100.08

B) 0.425 x 107

C) 42.5 x 105

D) 4.25 x 106

Show/Hide Answer

Writing Decimal Notation in Scientific Notation

Now let’s compare some numbers expressed in both scientific notation and standard decimal notation in order to understand how to convert from one form to the other. Take a look at the tables below. Pay close attention to the exponent in the scientific notation and the position of the decimal point in the decimal notation.

Large Numbers

Small Numbers

Decimal Notation

Scientific Notation

Decimal Notation

Scientific Notation

500.0

5 x 102

0.05

5 x 10-2

80,000.0

8 x 104

0.0008

8 x 10-4

43,000,000.0

4.3 x 107

0.00000043

4.3 x 10-7

62,500,000,000.0

6.25 x 1010

0.000000000625

6.25 x 10-10

To write a large number in scientific notation, move the decimal point to the left to obtain a number between 1 and 10. Since moving the decimal point changes the value, you have to multiply the decimal by a power of 10 so that the expression has the same value.

Let’s look at an example.

180,000. =      18,000.0  x  101

                                                             1,800.00  x 102

                                                                180.000 x 103

                                                                  18.0000 x 104

                                                                    1.80000 x 105

                                   180,000 = 1.8 x 105

Notice that the decimal point was moved 5 places to the left, and the exponent is 5.

The world population is estimated to be about 6,800,000,000 people. Which answer expresses this number in scientific notation?

A) 7 x 109

B) 0.68 x 1010

C) 6.8 x 109

D) 68 x 108

Show/Hide Answer

Advanced Question

Represent 1.00357 x 10-6 in decimal form.

A) 1.00357000000

B) 0.000100357

C) 0.000001357

D) 0.00000100357

Show/Hide Answer

To write a small number (between 0 and 1) in scientific notation, you move the decimal to the right and the exponent will have to be negative.

                             0.00004     =        00.0004   x  10-1

                                               000.004   x  10-2

                                                           0000.04   x   10-3

                                                           00000.4   x  10-4

                                                           000004.  x  10-5

                                       0.00004     =   4 x 10-5

0.82 x 10-6

Olin [163]3 years ago
3 0

Answer:

it should just be 34

Explanation:

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The Hall process for the production of aluminum involves the reaction of aluminum oxide with elemental carbon to give aluminum m
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Answer:

  • <u><em>1.7 × 10³ kg of ore.</em></u>

Explanation:

Call X the amount of aluminum ore mined to produce 1.0 × 10³ kg the aluminum metal.

Then, taking into account the yield of the reaction (82 % = 0.82) and the percent of aluminun in the ore (71% = 0.71), you can write the following equation:

  •  X         ×          71%                ×       82%     =     1.0 × 10³ kg

         ↑                      ↑                              ↑                     ↑

(mass of ore)    (% of Al in the ore)        (yield)        ( Al metal to obtain)

You must just simplify, solve and compute:

  • 0.71 × 0.82 × X = 1,000
  • X = 1,000 / (0.71 × 0.82) = 1,000 / 0.5822 = 1,717.6 Kg

Round to two significant figures; 1,700 kg = 1.7 × 10³ kg of ore ← answer.

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3 years ago
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