Scientific to Standard
Convert to standard notation:
4.7 xx10^4
47,000
Positive= move 4 to the right.
Convert to scientific notation: 234000
2.34xx10^5
(2xx10^3)xx(2xx10^4)
4xx10^7
First multiply the factor then multiply the powers by adding exponents per rules of exponents
Order the following from least to greatest.
3.5 xx 10^-7, 3.02 xx 10^-7, 3.11 xx 10^-7, 3.0 xx 10^-7
What is - compare the exponents first (all the same) so compare are the factors for size.
3.0 xx 10^-7, 3.02 xx 10^-7, 3.11 xx 10^-7, 3.5 xx 10^-7
Convert to standard notation:
8.932 xx10^-2
0.08932
Negative= move 2 to the left
Convert to scientific notation: 25,360
2.536xx10^4
(8xx10^10)/(4xx10^3)
2xx10^7
Divide factors: 8/4= 2
divide powers: 1010-3 = 107 Then 2 x 107
Compare using >, <, =
3.4 xx 10^2 3.04 xx 10^2
What is >
Same exponent so compare the 3.4 and 3.04. 3.4 is bigger
Convert to standard notation:
9.87xx10^-5
0.0000987
Negative exponent move 5 to the left
Convert to scientific notation: 0.00000008
8xx10^-8
(5xx10^8)xx(5xx10^3)
2.5xx10^12
First 5 x 5= 25, then 108+3= 1011 so 25 x 1011
Not scientific notation so 2.5 x 1011+1= 2.5 x 1012
Compare using >, <, =
3.45 xx 10^-5 3.4 xx 10^-5
What is >
same exponents compare the factor 3.45 and 3.4, 3.45 is larger
Convert to standard notation:
3xx10^6
3,000,000
Positive exponent decimal sits after the 3 so move 6 to the right.
Convert to scientific notation: 734,239
7.34239xx10^5
(1.2xx10^5)+(3.1xx10^4)
1.51xx10^5
Must have the same exponents, so make both to power of 5. So 3.1 x 104 goes to .31 x 105
Now add factors 1.2 + .31= 1.51 and keep power
1.51 x 105
Compare using >, < , =
0.000205 3.005 xx 10^-4
What is <
Turn 0.000205 into SN 2.05 x 10-4 so same exponent compare 3.005 and 2.005. 2.005 is smaller
Which of the numbers are not in scientific notation?
3.4xx10^8, 0.4xx10^-2, 6.25xx10^-2, 10.4xx10^4, 3xx10^3 4.5xx8^-5 0.52xx10^7
What is - Check the factor is it greater than or equal to 1 and less than 10. Check the power is the base 10.
0.4xx10^-2, 10.4xx10^4, 4.5xx8^-5 0.52xx10^7
Convert to scientific notation: 0.0003005
3.005 xx 10^-4
(6.3xx10^8)-(4.4xx10^7)
5.86xx10^8
Make the same power by making 4.4 X107 to .44 x 108
Subtract 6.3 - .44=5.86 (line up decimals and subtract) Then put them together- 5.86 x 108
Order the following from greatest to least.
3.0 xx 10^7, 4.5 xx 10^6, 4.5 xx 10^7, 9 xx 10^6
4.5 xx 10^7, 3.0 xx 10^7, 9 xx 10^6, 4.5 xx 10^6
Look first at the exponents, then compare the first factor.