Scientific Notation What is Scientific Notation n A

Scientific Notation

What is Scientific Notation? n. A way of expressing really big or really small numbers. n Most often used in “scientific” calculations where the analysis must be very precise.

Why use Scientific Notation? n Very large and very small numbers can be converted into scientific notation to express them in a more concise form. n Numbers expressed in scientific notation can be used in a computation with far greater ease.

Scientific notation consists of two parts: n. A number between 1 and 10 n. A power of 10 – The exponent may be positive or negative. N x 10 x

Are they in scientific notation? n 23. 98393 x 109 n 4. 19385930 x 104 n 9820. 1888 x 10 -3 n 2. 22221 x 10000 n 9. 002 x 100 n 3. 9992934 x 101 n 1. 01 x 1056 n 2. 39403 x 10 -23 n 9. 00078 x 10 -1

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is only one non-zero digit to the left of the decimal point. Ex: 2, 250, 000 2. 250000 Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. 2, 250, 000 2. 250000 2. 25 x 106

Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. Ex: . 0029 = 2. 9 x 10 -3

Example 1 n Given: 289, 800, 000 n Use: 2. 898 (moved 8 places) n Answer: 2. 898 x 108

Example 2 n Given: 0. 000567 n Use: 5. 67 (moved 4 places) n Answer: 5. 67 x 10 -4

Changing scientific notation to standard form

To change scientific notation to standard form… n Move the decimal point to the right for positive exponent 10. n Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places. )

Examples 3. 9456 x 106 (Positive exponent goes right. It’s a big number!) 3, 954, 600 8. 0965 x 10 -4 (Negative exponent goes left. It’s a tiny number!) . 00080965

Example 3 Given: 5. 093 x 106 Answer: 5, 093, 000 (moved 6 places to the right. Big Number)

Example 4 Given: 1. 976 x 10 -4 Answer: 0. 0001976 (moved 4 places to the left. Itty bitty number. )