Scientific notation division

A major benefit of presenting numbers in scientific notation is that it simplifies common arithmetic operations. The simplifying abilities of scientific notation cire most evident in multiplication and division. (As we note in the next section, addition and subtraction benefit from exponential notation but not necesscirily from strict scientific notation.)... 

To divide one number by another, put them both in standard scientific notation. Divide the first lefthand factor by the second, according to the rules of ordinary division. Divide the first righthand factor by the second, according to the division law for exponents—that is, by subtracting the exponent of the divisor from the exponent of the dividend to obtain the exponent of the quotient. 

Multiplying and dividing using scientific notation Multiplying and dividing also involve two steps, but in these cases the quantities being multiplied or divided do not have to have the same exponent. For multiplication, you multiply the first factors. Then, you add the exponents. For division, you divide the first factors. Then, you subtract the exponent of the divisor from the exponent of the dividend. 

Solve the following multiplication and division problems. Express your answers in scientific notation. 

Look at Fig re 7 to see how to solve multiplication and division problems involving scientific notation. The problems are the same as the two previous sample problems. 

For division of numbers in scientific notation, the coefficients are divided in the usual fashion. The exponent of the divisor is subtracted algebraically from the exponent of the number that is being divided. 

Multiplication and Division To multiply numbers expressed in scientific notation, we multiply Ni and N2 in the usual way, but add the exponents together. To divide using scientific notation, we divide and N2 as usual and subtract the exponents. 

The multiplication and division of numbers written in scientific notation can be done qnite simply by using some characteristics of exponentials. Consider the following multipUcation ... 

Multiplication and division calculations involving scientific notation are easily done using a hand calculator, t Table 1.4 gives the steps, the typical calculator procedures (buttons to press), and typical calculator readout or display for the division of 7.2 X 10 by 1.2 X 10 . 

Do the following divisions, and express each answer using scientific notation ... 

To multiply two numbers in scientific notation, you first multiply the two powers of ten by adding their exponents. Then you multiply the remaining factors. Division is handled similarly. You first move any power of ten in the denominator to the numerator, changing the sign of the exponent. After multiplying the two powers of ten by adding their exponents, you carry out the indicated division. 

Recall that zeros have special rules and may require a contextual interpretation. As a starting point, a number may be converted to scientific notation. If the zeros can be removed by this operation, then they were merely placeholders representing a multiplication or division by 10. For example, suppose an instrument produces a result of 0.001023 that can be expressed as 1.023 X 10. This demonstrates that the leading zeros are not significant, but the embedded zero is. 

Multiplication and division in scientific notation when numbers expressed in scientific notation are being multipUed, the following general rule is very useful ... 

When numbers have four or more digits to the left of the decimal point, they must have commas to help the reader to see quickly the thousands, millions, and so on, places. Only if the numbers are too cumbersome should powers-of-10 notation be used. When it is used, so-called engineering notation is preferred to scientific notation. In engineeiii notation, the power of 10 is always divisible by 3 (analogous to the commas mentioned above). In a column of num-bers that all refer to the same kind of property, the format should be the same for each entry. 

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