How do you write 350000350000 in scientific notation?
1 Answer
Explanation:
Start by writing your number in standard notation
three hundred fifty thousand
-> 350,000→350,000
Now, a number written in scientific notation will take the form
color(white)(aa)color(blue)(m) xx 10^(color(purple)(n) color(white)(a)stackrel(color(white)(aaaaaa))(larr))color(white)(acolor(black)("the")acolor(purple)("exponent")aa)aam×10naaaaaaa←−−−atheaexponentaa
color(white)(a/acolor(black)(uarr)aaaa)aa↑⏐ ⏐⏐aaaa
color(white)(color(black)("the")acolor(blue)("mantissa")a)theamantissaa
For normalized scientific notation, which is what you'll be dealing with in the vast majority of cases, you need to have
1 <= |color(blue)(m)| < 101≤|m|<10
In your case, you start with
350,000 * 10^0350,000⋅100
so you can say that you have
color(blue)(m) = 350,000" "and " " color(purple)(n) = 0m=350,000 and n=0
In order to write the number in scientific notation, you must divide it
1 <= color(blue)(m) < 101≤m<10
For every time you divide the number by
The trick here is that you divide the mantissa by
So, divide the mantissa by
(350,000)/10 * 10^0 * 10 = 35,000 * 10^1350,00010⋅100⋅10=35,000⋅101
Since
1 <= 35,000 color(red)(cancel(color(black)(<))) 10
you must repeat the procedure.
(35,000)/10 * 10^1 * 10 = 3,500 * 10^2
Once again, you have
1 <= 3,500 color(red)(cancel(color(black)(<))) 10
so you must repeat the procedure again
(3,500)/10 * 10^2 * 10 = 350 * 10^3
Repeat it again
350/10 * 10^3 * 10 = 35 * 10^4
Repeat it again
35/10 * 10^4 * 10 = 3.5 * 10^5
This time, you have
1 <= 3.5 < 10" "color(green)(sqrt())
so you can say that your original number written in scientific notation will look like this
350,000 = 3.5 * 10^5
Notice that the mantissa keeps the same number of sig figs as the number written in standard form, i.e.
