1 / 15

Section 1.6—Scientific Notation

Section 1.6—Scientific Notation. 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. Writing in Scientific Notation.

min
Download Presentation

Section 1.6—Scientific Notation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related