Chapter 2 Measurements 2.2 Scientific Notation Learning Goal Write a number in scientific notation. © 2014 Pearson Education, Inc.

Scientific Notation Scientific notation is used to write very large or very small numbers such as the width of a human hair, 0.000 008 m, which is also written as 8 × 10−6 m the number of hairs on a human scalp,100 000 hairs, which is also written as 1 × 105 hairs © 2014 Pearson Education, Inc.

Writing Numbers in Scientific Notation A number written in scientific notation contains a coefficient and a power of ten. coefficient power unit of ten 1.5 × 102 m The coefficient is at least 1 but less than 10. © 2014 Pearson Education, Inc.

Writing Numbers in Scientific Notation The number of spaces moved to obtain a coefficient between 1 and 10 is shown as a power of ten. 52 000. = 5.2 × 104 move decimal 4 spaces left 0.003 78 = 3.78 × 10−3 move decimal 3 spaces right © 2014 Pearson Education, Inc.

Some Powers of Ten © 2014 Pearson Education, Inc.

Some Measurements in Scientific Notation © 2014 Pearson Education, Inc.

Comparing Numbers in Standard and Scientific Notation Standard Format Scientific Notation Diameter of the Earth 12 800 000 m 1.28 × 107 m Mass of a human 68 kg 6.8 × 101 kg Diameter of a virus 0.000 000 3 cm 3 × 10−7 cm © 2014 Pearson Education, Inc.

Scientific Notation and Calculators You can enter a number written in scientific notation on many calculators using the EE or EXP key. © 2014 Pearson Education, Inc.

Scientific Notation and Calculators When a calculator display appears in scientific notation, it is shown as a number between 1 and 10, followed by a space and the power (exponent). © 2014 Pearson Education, Inc.

Scientific Notation and Calculators On many scientific calculators, a number is converted to scientific notation, using the appropriate keys. 0.000 52 2nd or 3rd function key SCI Key Key = 5.2 −04 or 5.2−04 = 5.2 × 10−4 Calculator display © 2014 Pearson Education, Inc.

Guide to Writing a Number in Scientific Notation © 2014 Pearson Education, Inc.

Learning Check Write the following number in the correct scientific notation, 0.000 058 g. © 2014 Pearson Education, Inc.

Move the decimal 5 places to the right, to give a coefficient of 5.8. Solution Write the following number in the correct scientific notation, 0.000 058 g. Step 1 Move the decimal point to obtain a coefficient that is at least 1 but less than 10. 0.000 058 Move the decimal 5 places to the right, to give a coefficient of 5.8. © 2014 Pearson Education, Inc.

Step 2 Express the number of places moved as a power of 10. Solution Write the following number in the correct scientific notation, 0.000 058 g. Step 2 Express the number of places moved as a power of 10. Moving the decimal 5 places to the right gives a power of −5. © 2014 Pearson Education, Inc.

Solution Write the following number in the correct scientific notation, 0.000 058 g. Step 3 Write the product of the coefficient multiplied by the power of 10 with the unit. 5.8 × 10−5 g © 2014 Pearson Education, Inc.

Select the correct scientific notation for each. A. 0.000 008 Learning Check Select the correct scientific notation for each. A. 0.000 008 (1) 8 × 106 (2) 8 × 10−6 (3) 0.8 × 10−5 B. 72 000 (1) 7.2 × 104 (2) 72 × 103 (3) 7.2 × 10−4 © 2014 Pearson Education, Inc.

Select the correct scientific notation for each. A. 0.000 008 Solution Select the correct scientific notation for each. A. 0.000 008 (Move the decimal 6 places to right.) (2) 8 × 10−6 B. 72 000 (Move the decimal 4 places to the left.) (1) 7.2 × 104 © 2014 Pearson Education, Inc.

Write each as a standard number. A. 2.0 × 10−2 Learning Check Write each as a standard number. A. 2.0 × 10−2 (1) 200 (2) 0.0020 (3) 0.020 B. 1.8 × 105 (1) 180 000 (2) 0.000 018 (3) 18 000 © 2014 Pearson Education, Inc.

Write each as a standard number. A. 2.0 × 10−2 (3) 0.020 B. 1.8 × 105 Solution Write each as a standard number. A. 2.0 × 10−2 (3) 0.020 B. 1.8 × 105 (1) 180 000 © 2014 Pearson Education, Inc.