1. All non-zero digits are always significant.
2. Zeroes between other significant figures are significant.
3. Trailing zeroes without a decimal point are not significant.
4. Trailing zeroes after a decimal point are significant.
5. Leading zeroes that come before a non-zero number are not significant.
1. 2598 has four significant figures.
2. 25005 has five significant figures.
3. 160 has two significant figures.
4. 45.800 has five significant figures.
5. 00.00589 has three significant figures.
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When we convert a long number to scientific notation we need to identify the significant digits.In 2010000 we have only three significant digits (201) as the remaining zeros wont change the value of the number once we place it in scientific notation.The rules of SN (Scientific Notation) state that our number must be between 1-9 so in order to make it between 1-9 we have to move the decimal place to the left.With moving decimals to the left the exponent that will be placed by x 10N will result in a positive number. When we move to the right we will find a negative number.2010000 x 100201000.0 x 10120100.00 x 1022010.000 x 103201.0000 x 10420.10000 x 1052.01 x 106So 2010000 in scientific notation is 2.01 x 106And in Computerese...This can also be expressed as 2.01E6
To convert a number to scientific notation, move the decimal point right or left to make the number greater than or equal to one but less than ten, and record the number of positions moved as a power of 10 - the exponent. That is, if the decimal point moves to the left by n positions, then the exponent is 10n. If the decimal point moved to the right by npositions, the exponent is 10-n (note the minus symbol).For instance, the number 123,456,000,000 is larger than 10, so we move the decimal point 11 positions to the left to get 1.23456, which is greater than or equal to one, but less than ten. Since we moved the decimal point to the left by 11 positions, the exponent is 1011 (ten raised to the eleventh power, which is 100,000,000,000) so the scientific notation for 123,456,000,000 becomes 1.23456x1011.If the original number were 0.000000123456, we need to move the decimal point to the right by seven positions to get 1.23456 (greater than or equal to one but less than ten). The exponent is therefore 10-7, thus the scientific notation for 0.000000123456 is 1.23456x10-7.To convert from scientific notation to standard notation, we simply reverse the process. If the exponent is a positive power of 10, we multiply by the exponent. Thus 1.23456x1011 is 1.23456 x 100,000,000,000 which is 123,456,000,00. If the exponent is a negative power of 10, we divide by the exponent. Thus 1.23456x10-7 is 1.23456 / 10,000,000 which is 0.000000123456.Note that scientific notation is only useful when you are not interested in the least significant portion of a number. For instance, a value such as 123,456,789,123,456,789,123,456,789 is better notated in full if you want the highest degree of accuracy. Scientific notation is generally only used to make the notation of an extremely large (or extremely small) number more concise. So 123,456,789,123,456,789,123,456,789 might be reduced to a more concise form such as 1.23456789x1026. This then equates to 123,456,790,000,000,000,000,000,000 in standard notation, which is clearly not the same value we started out with. In other words, the degree of accuracy is determined by the number of decimal places you retain in the scientific notation.
The rules of PEMDAS are 1. Parenthesis anything in them you do first. 2. Exponents those little numbers next to the number telling you to multiply the number by itself a certain number of times 3. Multiplication and Division whichever comes first and 4. Addition and Subtraction whichever comes first. If there is an exponent next to parenthesis but there is no number that means the answer to the parenthesis has to be the thing that the exponent is next to. All of the rules apply inside of the parenthesis as well. If there is a number next to the parenthesis not followed by a symbol multiply the answer to the parenthesis by that number.
(positive number) x (positive number) = positive number (positive number)/(positive number) = positive number (positive number) x ( negative number) = negative number (positive number)/( negative number) = negative number (negative number) x (negative number) = positive number (negative number)/(negative number) = positive number
The rules of algebra: more specifically, it is the the existence of a multiplicative inverse for all non-zero values.