sdrta.netists regularly work v numbers that space extremely large or extremely small. Forexample, there are 10,300,000,000,000,000,000,000 carbon atoms in a 1-carat diamond eachof which has actually a fixed of 0.000,000,000,000,000,000,000,020 grams. It is impossible tomultiply these numbers with many calculators because they can"t expropriate either number as itis composed here. To do a calculation prefer this, the is crucial to express this numbersin scientific notation, together a number between 1 and also 10 multiply by 10 elevated tosome exponent.
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Some of the basics that exponential mathematics are provided below.
|Any number raised to the zero power is same to 1.||1�= 1||10�= 1|
|Any number raised to the very first power is equal to itself.||11 = 1||101 = 10|
|Any number elevated to the nth power is equal to the product of the number times itself n-1 times.|
|22 = 2 x 2 = 4||105 = 10 x 10 x 10 x 10 x 10 = 100,000|
|Dividing through a number increased to one exponent is the same as multiplying by that number raised to an exponent of opposing sign.|
Converting to scientific Notation
The following dominion can be provided to convert numbers right into scientific notation: Theexponent in clinical notation is same to the number of times the decimal point must bemoved to create a number in between 1 and 10. In 1990 the population of Chicago was6,070,000 �1000. To transform this number to clinical notation we relocate the decimal pointto the left 6 times.
|6,070,000 = 6.070 x 106|
To translate 10,300,000,000,000,000,000,000 carbon atoms right into scientific notation, wemove the decimal point to the left 22 times.
10,300,000,000,000,000,000,000 = 1.03 x 1022
To transform numbers smaller sized than 1 into scientific notation, we need to move the decimalpoint to the right. The decimal suggest in 0.000985, because that example, should be relocated to the rightfour times.
0.000985 = 9.85 x 10-4
Converting 0.000,000,000,000,000,000,000,020 grams per carbon atom right into scientificnotation requires moving the decimal allude to the right 23 times.
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0.000,000,000,000,000,000,000,020 = 2.0 x 10-23
The main reason for converting numbers into scientific notation is come makecalculations v unusually large or tiny numbers much less cumbersome. Due to the fact that zeros room nolonger provided to collection the decimal point, every one of the number in a number in scientific notationare significant, as shown by the following examples.
|2.4 x 1022||2 far-ranging figures|
|9.80 x 10-4||3 significant figures|
|1.055 x 10-22||4 far-reaching figures|
|Practice trouble 8 |
Convert the following numbers into scientific notation.