Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematics of radio engineering wikipedia , lookup
Principia Mathematica wikipedia , lookup
Abuse of notation wikipedia , lookup
Bra–ket notation wikipedia , lookup
Location arithmetic wikipedia , lookup
History of mathematical notation wikipedia , lookup
Approximations of π wikipedia , lookup
Musical notation wikipedia , lookup
Large numbers wikipedia , lookup
Big O notation wikipedia , lookup
1.6 Notes Scientific Notation A number is expressed in scientific notation, when it is written as the product of a number between 1 and 10, and a power of 10. Standard Form → Scientific Notation Find a decimal point (or add one at the end if there is none). Move the decimal point along the number to a new position, Stop when only one non-zero digit left in front of the decimal point. The # of moves is recorded as the power of 10 . ? Is my number in standard form small or BIG number???? o If it was a decimal less than 1 (small #), the o If it was a number greater than 10 (BIG #), the exponent will be NEGATIVE . exponent will be POSITIVE Example: 5,700,000 = 5.7 × Example: 0.000072 = 7.2 × Scientific Notation → Standard Form Positive exponent: Multiply the number by a power of 10; OR move the decimal point to the right as many spaces as the exponent . Fill in the spaces at the end with zeros . Remember: we want a BIG number! Example: Negative exponent: The result will be less than 1 . Move the decimal point to the left as many spaces as the exponent . Fill in the spaces in front with zeros . Example: 1.0305 × 4.309 × = 0.0004309 103,050,000 Comparing Numbers in Scientific Notation: DO NOT rewrite them in standard form! 1) FIRST compare the exponents. Greater exponent means greater number. 2) ONLY if the exponents are the same, compare their decimals. Compare 1. 6.23 × and 8.912 × 2. 5.15 × > or 6.35 × 3. 3.28 × and 4.25 × > < Order the real numbers from least to greatest a) 2.81 × 2.72 × ; 2.01 × ; 2.81 × ; 2.72 × ; 9.45 × ; 9.45 × . ; 2.01 × b) 135%, 13.5, , 3.9 × 1.35(1) 13.5(4) 4.555… (3) Answer: 135%, √ , , √ 390(5) 4.472… (2) , 13.5, 3.9 ×