Scientific Notation

Miura-Aguinaldo

Albano

Physical Science

Scientific Notation

Expresses numbers as a set of digits greater than 1 but less than 10 multiplied by a power of 10. This is accomplished by moving the decimal point on the number and multiplying by 10^x, where x represents the number of times the decimal needed to be moved

ex:

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3,000,000,000 cm =

0.000000000000009 mm =

If the decimal moves to the left, then it's a positive exponent

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3 x 10⁹cm

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If the decimal moves to the right then it's a negative exponent

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9 x 10^-15 mm

Multiplying numbers written in Scientific Notation

1.00 x 10¹ x 3.66543 x 10³

Multiply numbers first 1.00 x 3.66543 =

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Add exponents together for powers of 10

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3.67 x 10⁴

3.66543

and round to proper S.F. = 3.67

10¹⁺³

Dividing numbers written in Scientific Notation

9.3 x 10¹ / 3 x 10³

Divide numbers first 9.3 / 3 = 3.1

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Subtract exponents for powers of 10

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3 x 10^-2

and round to proper S.F. = 3

10^1-3

Adjusting for proper format

Sometimes, the numbers don't work out in proper scientific notation:

3.0 x 10⁶ x 6.0 x 10⁹ = 18 x 10¹⁵

If this is the case, convert the first number properly, then adjust the exponent

18 x 10¹⁵ = 1.8 x 10¹ x 10¹⁵

1.8 x 10¹⁺¹⁵ = 1.8 x 10¹⁶

Adding and subtracting

Numbers written in scientific notation can only be added or subtracted if the exponent is the same. You might need to take one number out of scientific notation to make the exponents match, carry out the calculation, then put the answer back into scientific notation.

Practice Problems

Express the following in scientific notation:

1. 678,000 =
2. 0.000452 =
3. 43,000 =
4. 0.0000095 =
5. 70,200 =

Practice Problems

Express the following as a regular number

1. 1.8 x 10⁵ =
2. 5.36 x 10^-9 =
3. 8.2 x 10¹¹ =
4. 7.3 x 10^-4 =
5. 3.94 x 10¹⁴ =

Practice Problems

Calculate and round to the proper sig figs

1. (3.0 x 10⁶) x (6.0 x 10⁹) =
2. (7.4 x 10^-3) x (9.0 x 10²)=
3. (5.7 x 10¹⁰) x (8.2 x 10⁴)=
4. (3.5 x 10^-5) / (2.1 x 10⁷) =
5. (8.4 x 10¹³) / (4.9 x 10⁸)=