what is scientific notation be able to work calculator
 | Math Skills Review Scientific Note |
Scientific notation 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 ten -9. So, how does this work?
We can think of 5.6 x 10 -9 as the product of two numbers: five.half-dozen (the digit term) and 10 -9 (the exponential term).
Here are some examples of scientific notation.
| 10000 = one x 10four | 24327 = two.4327 x x4 |
| 1000 = 1 x 103 | 7354 = 7.354 x 103 |
| 100 = 1 x 10two | 482 = four.82 10 102 |
| 10 = 1 ten ten1 | 89 = 8.9 x 10i (not normally done) |
| 1 = ten0 | |
| 1/10 = 0.1 = ane x 10 -1 | 0.32 = 3.2 x 10 -1 (non unremarkably done) |
| 1/100 = 0.01 = 1 x 10 -2 | 0.053 = 5.3 x 10 -ii |
| 1/yard = 0.001 = 1 ten 10 -3 | 0.0078 = seven.eight x 10 -3 |
| ane/10000 = 0.0001 = one 10 x -4 | 0.00044 = four.4 10 ten -iv |
Every bit y'all tin see, the exponent of 10 is the number of places the decimal signal must be shifted to give 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 bespeak is shifted that number of places to the left.
In scientific annotation, the digit term indicates the number of significant figures in the number. The exponential term only places the decimal indicate. As an example,
How to do calculations:
On your scientific reckoner:
Make certain that the number in scientific notation is put into your calculator correctly.
Read the directions for your particular figurer. For inexpensive scientific calculators:
- Punch the number (the digit number) into your calculator.
- Push the EE or EXP push. Do Non use the x (times) button!!
- Enter the exponent number. Use the +/- button to change its sign.
- Voila! Care for this number normally in all subsequent calculations.
To cheque yourself, multiply half-dozen.0 x 10five times 4.0 x 103 on your calculator. Your answer should be two.four 10 10ix.
On your cheap non-scientific calculator:
Y'all will need to be familiar with exponents since your calculator cannot take care of them for y'all. For an introduction to rules concerning exponents, see the department on Manipulation of Exponents.
Improver and Subtraction:
- All numbers are converted to the aforementioned power of 10, and the digit terms are added or subtracted.
- Case: (4.215 ten 10 -2) + (three.2 x 10 -4) = (4.215 x 10 -2) + (0.032 x 10 -2) = four.247 x 10 -ii
- Instance: (viii.97 x 104) - (2.62 x ten3) = (viii.97 x 10iv) - (0.262 10 10four) = viii.71 x 104
- The digit terms are multiplied in the normal way and the exponents are added. The end issue is changed so that there is only one nonzero digit to the left of the decimal.
- Example: (3.4 x ten6)(4.2 10 ten3) = (3.4)(4.ii) ten 10(6+3) = 14.28 x 10ix = 1.4 x 1010
(to two significant figures) - Example: (6.73 10 10 -5)(2.91 x x2) = (6.73)(2.91) ten 10(-5+2) = xix.58 x x -3 = 1.96 x 10 -2
(to 3 significant figures)
Division:
- The digit terms are divided in the normal way and the exponents are subtracted. The quotient is inverse (if necessary) so that there is only 1 nonzero digit to the left of the decimal.
- Example: (6.4 x 106)/(8.9 x 102) = (6.four)/(8.9) x 10(vi-ii) = 0.719 x 104 = 7.ii x xiii
(to two significant figures) - Example: (iii.2 x 103)/(v.7 x x -2) = (3.2)/(5.7) ten 103-(-2) = 0.561 x 105 = 5.6 10 104
(to ii 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 ability.
- Instance: (2.4 x 10four)3 = (2.4)iii x x(4x3) = xiii.824 x 1012 = 1.4 x ten13
(to 2 significant figures) - Example: (half-dozen.53 10 10-3)ii = (6.53)ii 10 10(-iii)x2 = 42.64 x 10 -6 = 4.26 ten 10 -five
(to 3 meaning figures)
Roots of Exponentials:
QUIZ:
| Question 1 | Write in scientific notation: 0.000467 and 32000000 |
| Question 2 | Express 5.43 x x -3 as a number. |
| Question three | (4.5 x 10 -fourteen) ten (v.2 x 103) = ? |
| Question 4 | (six.i x 10v)/(1.two x 10 -3) = ? |
| Question 5 | (3.74 x 10 -3)4 = ? |
| Question 6 | The 5th root of 7.xx x 1022 = ? |
Answers: (1) 4.67 x 10 -four; 3.two x 107 (ii)0.00543 (3) ii.three x 10 -10 (2 significant figures) (4) 5.one x 108 (2 significant figures) (5) 1.96 x 10 -10 (3 meaning figures) (6) 3.73 x x4 (3 significant figures)
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Source: https://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
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