scientific notation: 3.4 * 10^4
decimal notation 34000.0
Step-by-step explanation:
So there are three parts, first the conversion and then making it into scientific notation and decimal notation.
First the conversion, to do so you want the conversion factor. What that is is a fraction that relates the two units. so cg and mg or centigrams and miligrams. You can even choose a middle step, and if you do I would say grams. Mostly if it is maybe not simple for you to jump to there are 10 mg in a cg, you should know there are 100 cg in a gram and 1000 mg in a gram.
I will use the two step conversion. so first cg to gram. it will either be 100 cg / 1 g or 1 g/ 100 cg. You decide which by what unit you want to get rid of. here you want to get rid of cg, so cg is on the bottom. You can think of it like canceling out, how in something like 5x/x the xs cancel out and it becomes 5/1 or 5.
so the first conversion is 3400 cg * 1 g/ 100 cg = 3400/100 g = 34g
similarly we convert to mg with 1000 mg/ 1 g since we want to get rid of grams so it is now 34 g * 1000 mg/ 1 g = 34 * 1000 mg = 34000 mg
you could have done both at once too like this.
3400 cg * 1 g/ 100 cg * 1000 mg/ 1 g =
3400 * 1/100 * 1000/1 mg =
3400 * 1000/100 mg =
3400 * 10 mg =
34000 mg
and of course if you knew there were 10 mg in a cg you could just do 3400 cg * 10 mg/ 1 cg = 34000 mg
Now for scientific notation. All whole numbers have a decimal point on their right, so you could write 34000 as 34000.0. scientific notation then multiplies or divides the number by 10 until you have a new number between 1 and 10. You just have to make sure to keep doing the opposite elsewhere. so with 34000 since it is larger than 1 we divide it.
34000.0
3400.0 * 10
340.0 * 10 * 10
34.0 * 10 * 10 * 10
3.4 * 10 * 10 * 10 * 10
Now we have a number between 1 and 10. it's still kind of long though, so since you have 10 * 10 * 10 * 10, you can express this as an exponent, since 2^2 is 2 * 2 and 2^3 is 2 * 2 * 2. with 4 10s you get 10^4. So the scientific notation form is 3.4 * 10^4
Another way to do it is just move the decimal point and that is the exponent you put on the 10.
34000.0
3400.0
340.0
34.0
3.4
So you moves it left 4 times, this makes the exponent positive 4. if you move it right, like on .00021 the exponent would be negative. but moving it left 4 times on 34000.0 lets us know it is 3.4 * 10^4
Decimal notation I'm pretty sure is just the form with a decimal at the end, which we found. 34000.0
