5 000 000 = 5 x 1 000 000 right?

1 000 000 = 10^6 because 10x10x10x10x10x10 = 1 million (notice how the number of 0’s determines the exponent for the 10?)

So 5 000 000 = 5 x 10^6

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For 0.00456, let’s go through some basic rules about scientific notation:

There is always ONE number before the decimal point; no more, no less. There may or may not be a decimal point written, but you can only have ONE number in its respective place. This means the first part of your scientific notation will be:

4.56

See? Only ONE number before the decimal point (oh, and it can’t be 0).

Now you have to figure out how far you moved the decimal point. I can’t demonstrate it here, but if you do “bumps” underneath the numbers as you go from the decimal point’s original place to its new place (right after the 4), you make 3 such bumps. So, 10^-3. Why negative? Because you need to. I can explain it separately in a message, if you like.

So, your scientific notation will be 4.56 x 10^-3

Right now, the decimal is after the last zero. You must move it til it is between the 5 and the 0 next to it. That means you move it 6 spaces. Therefore, you would write 5 X 10^6

.00456

You must move the decimal til it is on the right side of the first non-zero digit, which is 4. To get there, you are moving the decimal 3 spaces. Therefore the answer is 4.56 X 10^-3

*Keep in mind, when you are moving the decimal to the left, the exponent will be positive. When you are moving it to the right, the exponent will be negative.

.0056

The first main number is 5, since you cant have a number to the 0 power. If you put the decimal point between the 5 and the 6, then move it to the end of the number, it becomes 5.6 to the 1st.

Good luck.

0.00456 = 4.56 X 10^3

.00456=4.56 x 10^-3

Just so you know, David M is wrong. After 12 grades of math including calculus he doesn’t know that a decimal value always has 10 to the power of a negative!! Remember that so that you don’t make the same mistake. Hope I helped!!

4.56 X 10^-3

For the second one: 0.00456

0.00006 + 0.00050 + 0.00400 + 0.00000 + 0.00000

[five times ten to the sixth power; sixth power because there are six zeroes. ;)]

4.56*10^(-3)

it’s not hard, you just have to know the rules.