Section 1.6—Scientific Notation

1. Section 1.6—Scientific Notation

2. Scientific Notation • Scientific Notation is a form of writing very large or very small numbers in a faster format • Scientific notation uses powers of 10 to shorten the writing of a number.

3. Writing in Scientific Notation • The decimal point is put behind the first non-zero number • The power of 10 is the number of times it moved to get there • A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent

4. Example #1 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m Example: Write the following numbers in scientific notation.

5. Example #1 4 1.2457656  10 m 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m Example: Write the following numbers in scientific notation. -5 6.5423  10 g 2 1.2890  10 g -7 7.532  10 m The decimal is moved to follow the first non-zero number The power of 10 is the number of times it’s moved

6. Large original numbers have positive exponents Example #1 4 1.24567656  10 m 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m Example: Write the following numbers in scientific notation. -5 6.5423  10 g 2 1.2890  10 m -7 7.532  10 m Tiny original numbers have negative exponents

7. Reading Scientific Notation • A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller • Move the decimal place to make the number bigger or smaller based on the power of ten

8. Example #2 1.37  104 m 2.875  102 g 8.755  10-5 g 7.005 10-3 m Example: Write out the following numbers.

9. Example #2 1.37  104 m 2.875  102 g 8.755  10-5 g 7.005 10-3 m 13700 m Example: Write out the following numbers. 287.5 g 0.00008755 g 0.007005 m Move the decimal “the power of ten” times Positive powers = big numbers. Negative powers = tiny numbers

10. Scientific Notation & Significant Digits • Scientific Notation is more than just a short hand. • It is also a more convenient way to look at our significant digits.

11. Take a look at this… • Write 120004.25 m with 3 significant digits 120004.25 m 8 significant digits 120000. m 6 significant digits 120000 m 2 significant digits 1.20  105 m 3 significant digits 120. m Remember…120 isn’t the same as 120000! Just because those zero’s aren’t significant doesn’t mean they don’t have to be there! This answer isn’t correct!

12. Examples #3 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs Example: Write the following numbers in scientific notation.

13. Examples #3 1.20 × 105 g 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs Example: Write the following numbers in scientific notation. 2.3 × 10-4 m 1.206 × 104 mL 2.4 × 10-7 g Move the decimal after the first non-zero number Start counting significant figures from that first non-zero number Round when you get the wanted number of significant digits Remember—large numbers are positive powers of ten & tiny numbers have negative powers of ten!

14. Let’s Practice 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write the following numbers in scientific notation. 1.34 × 10-3 g 2.009  10-4 mL 3.987  105 g 2.897  103 m Example: Write out the following numbers

15. Let’s Practice 7.7 × 10-4 g 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write the following numbers in scientific notation. 1.20 × 105 m 2.391 × 105 mL 7.80 × 10-6 g 0.00134 g 1.34 × 10-3 g 2.009  10-4 mL 3.987  105 g 2.897  103 m Example: Write out the following numbers 0.0002009 mL 398700 g 2897 m