Atom Scientific Notation Worksheet W 313 Convert the following numbers into scientific notation

Atom Scientific Notation Worksheet W 313 Convert the following numbers into scientific notation: 1) 923 2) 0.00425 3) 4523000 4) 0.94300 5) 6750. 6) 92.03 7) 7.80 B) 0.00000032 Convert the following numbers into standard notation: 9) 3.92400 x 10 10) 9.2 x 106 11) 4.391 x 10 12) 6.825 x 10- 13) 4.6978 x 10* 14) 8.36 x 10 15) 2.46 x 105 16) 8.8 x 102 Whery Center Stappertsen

The Correct Answer and Explanation is :

Scientific notation is a method of expressing numbers as a product of a coefficient and a power of ten, which is particularly useful for representing very large or very small numbers. The general form is ( a \times 10^n ), where ( 1 \leq |a| < 10 ) and ( n ) is an integer.

Converting to Scientific Notation:

1. 923: Move the decimal point two places to the left: ( 9.23 \times 10^2 ).
2. 0.00425: Move the decimal point three places to the right: ( 4.25 \times 10^{-3} ).
3. 4,523,000: Move the decimal point six places to the left: ( 4.523 \times 10^6 ).
4. 0.94300: Move the decimal point one place to the right: ( 9.4300 \times 10^{-1} ).
5. 6,750.: Move the decimal point three places to the left: ( 6.750 \times 10^3 ).
6. 92.03: Move the decimal point one place to the left: ( 9.203 \times 10^1 ).
7. 7.80: The number is already between 1 and 10: ( 7.80 \times 10^0 ).
8. 0.00000032: Move the decimal point seven places to the right: ( 3.2 \times 10^{-7} ).

Converting to Standard Notation:

9. 3.92400 × 10^5: Move the decimal point five places to the right: 392,400.
10. 9.2 × 10^6: Move the decimal point six places to the right: 9,200,000.
11. 4.391 × 10^-3: Move the decimal point three places to the left: 0.004391.
12. 6.825 × 10^-4: Move the decimal point four places to the left: 0.0006825.
13. 4.6978 × 10^4: Move the decimal point four places to the right: 46,978.
14. 8.36 × 10^1: Move the decimal point one place to the right: 83.6.
15. 2.46 × 10^-5: Move the decimal point five places to the left: 0.0000246.
16. 8.8 × 10^2: Move the decimal point two places to the right: 880.

In scientific notation, numbers are expressed as a coefficient multiplied by a power of ten. The coefficient is a number greater than or equal to 1 and less than 10, and the exponent indicates how many places the decimal point has been moved. A positive exponent shows the decimal point was moved to the left (indicating a large number), while a negative exponent shows it was moved to the right (indicating a small number). This notation simplifies the representation and calculation of very large or very small numbers, making it easier to read, write, and understand them.