Negative Exponents In Scientific Notation
 | Math Skills Review Scientific Notation |
Scientific annotation is the way that scientists hands handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.half dozen x 10 -9. So, how does this work?
We can think of 5.six x ten -9 as the product of two numbers: 5.half-dozen (the digit term) and 10 -9 (the exponential term).
Hither are some examples of scientific note.
| 10000 = ane ten 10iv | 24327 = 2.4327 x 104 |
| 1000 = 1 x xiii | 7354 = 7.354 x 103 |
| 100 = 1 10 10two | 482 = 4.82 x 102 |
| 10 = i ten tenane | 89 = eight.9 x 10one (not usually done) |
| 1 = ten0 | |
| 1/10 = 0.i = 1 x 10 -i | 0.32 = 3.2 x ten -1 (not usually done) |
| i/100 = 0.01 = one x 10 -2 | 0.053 = five.iii 10 10 -two |
| 1/chiliad = 0.001 = i x x -3 | 0.0078 = seven.eight ten 10 -three |
| 1/10000 = 0.0001 = 1 10 x -4 | 0.00044 = iv.4 x ten -4 |
As you tin can see, the exponent of 10 is the number of places the decimal point must be shifted to requite the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left.
In scientific notation, the digit term indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example,
How to do calculations:
On your scientific figurer:
Make sure that the number in scientific notation is put into your computer correctly.
Read the directions for your particular calculator. For cheap scientific calculators:
- Punch the number (the digit number) into your estimator.
- Push the EE or EXP button. Do NOT utilize the x (times) button!!
- Enter the exponent number. Use the +/- button to change its sign.
- Voila! Treat this number normally in all subsequent calculations.
To cheque yourself, multiply 6.0 10 xfive times 4.0 ten ten3 on your calculator. Your respond should be ii.four ten ten9.
On your inexpensive not-scientific calculator:
You volition need to be familiar with exponents since your calculator cannot take care of them for yous. For an introduction to rules concerning exponents, run into the section on Manipulation of Exponents.
Addition and Subtraction:
- All numbers are converted to the same power of ten, and the digit terms are added or subtracted.
- Example: (iv.215 x 10 -2) + (iii.2 10 ten -4) = (4.215 x 10 -two) + (0.032 x 10 -2) = 4.247 ten 10 -2
- Example: (8.97 ten 104) - (2.62 x 10iii) = (8.97 x 104) - (0.262 ten x4) = 8.71 x ten4
- The digit terms are multiplied in the normal manner and the exponents are added. The end result is changed so that there is only one nonzero digit to the left of the decimal.
- Example: (3.4 10 106)(4.2 x 103) = (3.4)(4.2) x x(half dozen+3) = 14.28 ten 109 = 1.4 x 10x
(to 2 significant figures) - Case: (6.73 x ten -5)(2.91 x xii) = (six.73)(2.91) x ten(-5+2) = 19.58 ten ten -3 = 1.96 x ten -ii
(to 3 significant figures)
Division:
- The digit terms are divided in the normal style and the exponents are subtracted. The quotient is changed (if necessary) and then that in that location is but one nonzero digit to the left of the decimal.
- Instance: (6.four x 106)/(8.nine x tenii) = (6.4)/(eight.9) ten x(6-ii) = 0.719 x 10iv = vii.2 x 103
(to 2 significant figures) - Example: (three.two x 10three)/(5.7 x ten -2) = (iii.2)/(v.seven) x 103-(-2) = 0.561 x 105 = five.6 x 104
(to 2 significant figures)
Powers of Exponentials:
- The digit term is raised to the indicated power and the exponent is multiplied past the number that indicates the power.
- Example: (2.4 x 10iv)three = (2.4)3 x ten(4x3) = 13.824 ten x12 = 1.4 ten 1013
(to 2 significant figures) - Example: (6.53 x 10-3)2 = (vi.53)two x 10(-iii)x2 = 42.64 x 10 -6 = iv.26 10 x -five
(to three significant figures)
Roots of Exponentials:
QUIZ:
| Question ane | Write in scientific notation: 0.000467 and 32000000 |
| Question 2 | Express v.43 10 10 -3 as a number. |
| Question 3 | (4.v x 10 -14) x (5.two x 10three) = ? |
| Question iv | (6.1 x 105)/(1.2 x 10 -3) = ? |
| Question five | (iii.74 x 10 -iii)4 = ? |
| Question half dozen | The 5th root of 7.twenty x 1022 = ? |
Answers: (i) 4.67 x ten -4; 3.2 x 107 (two)0.00543 (3) 2.3 x ten -10 (2 significant figures) (iv) 5.1 x 10eight (ii significant figures) (v) 1.96 x 10 -ten (3 pregnant figures) (6) 3.73 10 x4 (three significant figures)
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Negative Exponents In Scientific Notation,
Source: https://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html#:~:text=A%20negative%20exponent%20shows%20that,only%20places%20the%20decimal%20point.
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