6 big and tiny numbers

6.1 clinical notation

Understanding just how your calculator displays and handles very huge and very little numbers is crucial if you room to translate the outcomes of calculations correctly. This section concentrates on a means of representing numbers recognized as scientific notation.

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Before friend start placed your calculator right into the float mode, so that will screen up to about 10 digits and also return come the home display screen ready to do some calculations.

What answer would certainly you intend if girlfriend square 20 million? How plenty of zeros would the answer have? If you perform this on paper, girlfriend should finish up v 4 complied with by 14 zeros. However your calculator might not be able to display 14 figures, if the is set to 10 figures. Therefore input this calculation right into your calculator and see what that does:

20000000

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You will certainly probably obtain something choose 4e14. The notation e14 should be check out as 10 to the strength 14 (or 10 to the 14) which means fourteen 10s multiply together. The is composed as 1014. Therefore the calculator price of 4e14 is 4 × 1014, i m sorry is quick for 400000000000000.

The number 14, the is the power of 10, is likewise called the exponent and method the number of 10s which are multiplied together. The letter E in 4e14 is offered to median exponent.

Now rather of 20 million squared, what would 90 million squared be? What would you expect? try it on your calculator and see.

Since 20 million squared to be 4 × 1014, you could expect the 90 million squared would certainly be 81 × 1014.

However, the calculator mirrors a various answer. Shot it and also see.

The calculator"s price of 8.1e15 or 8.1 × 1015 is in reality the same number together 81 × 1014.

Both these numbers stand for 8 100 000 000 000 000.

However, as soon as a number is written utilizing a scientific notation the convention is to usage a number between 1 and also 10 prior to the exponent. So here, rather of 81 × 1014, the number 8.1 is offered with one extra power of 10.

Another method of interpreting 8.1 × 1015 is come imagine the the decimal point in the number 8.1 need to be relocated 15 areas to the right, pour it until it is full in as many zeros together necessary.


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(a) The rate of light measured in meters every second, is about 300 million (300 000 000) meters every second. What is this number in clinical notation?

(b) Einstein"s well known equation claims that E = mc2, the power E (in joules) associated with a fixed of m kilograms is equal to m multiplied by c squared, where c is the speed of irradiate (in meters per second). Using the value of c offered in your answer to part (a), occupational out the worth of E in clinical notation because that a mass of 1 kilogram.

(c) The street from the planet to the sunlight is about 149 million kilometres. What is this number in clinical notation?

(d) What is the biggest number your calculator can handle? for example, enter any type of number and also keep squaring. How far can friend go prior to the calculator displays an error message?


Answer

(a) 300 000 000 = 3 × 108

(b)

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(c)

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(d) The TI-84 calculator cannot take care of numbers with exponents of 100 or more. An alert that the calculator produces a article saying ERR:OVERFLOW.


Small numbers very close to zero can likewise be expressed in clinical notation. For example, enter a straightforward starting worth such together 4.3 and also then consistently divide by 10. This can be excellent by pressing

4 . 3

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1 0

And therefore on.

Watch closely how the numbers go: 4.3, .43, .043, .0043, etc. Then at some allude the display will jump right into scientific notation. Different calculators use different methods the displaying scientific notation. Look at in your calculator handbook to examine how her calculator displays scientific notation and also compare it with that used by the TI-84, which gives .00043 together 4.3e−4.

The e−4 part way that the decimal allude in the number 4.3 have to be moved four places come the left, which calls for the insertion that some extr zeros.


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What wake up to the result if friend keep dividing by 10? You have to see the exponent adjust from −4 come −5 to −6, and also so on. As the an unfavorable exponent gets larger, the matching decimal number it s okay smaller.

As with big numbers, the notation e−4 must be check out as ‘10 come the strength −4’ (or just ‘10 to the minus 4’).

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Do not issue about an unfavorable powers of 10 because that the moment. Just think the the notation as a method of writing down little numbers wherein the an unfavorable sign reminds you that the decimal suggest must be relocated to the left. Right here is one more example.