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.

You are watching: How is scientific notation useful?

Exponent Review

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.

See more: Which One Of The Pairs Of Angles Below Is Adjacent, 2 And 4 1 And 3 1 And 2 3 And 1

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.