Just started learning about the scientific notation, and its actually quite easy, but I don't know why im still struggling with it.

For example it says express the following measurements in scientific notation:

5800m

The answer is 5.8 * 10^3

What confuses me is that how do you know where to put the decimal thing. It can't be anywhere in the Zeros? I was also confused on how they got the power to the three thing, but I figured that you have to imagine the decimal being at the end of 5800, then you move 3 decimal places till you reach 5.8. I want to know an easier way to do this, cause I think Im thinking too much.

For scientific Notation, when expressing the number it cannot be greater then10. You usually put the decimal in the tenths spot such as 1.0, 2.0, 3.0 etc. you would imagine that your decimal is at the end of the number and then move your decimal toward the end. the exponent refers to what direction to express it as a whole number and how many decimals to move. if it was negative that means you move the decimal in the left direction such as... 1.23X10^-3 is really 0.00123 or 1.23X10^3 is 1230.

hope that helps.

Understanding scientific notation may seem difficult at first, but with practice, it becomes easier. Let's break down the steps to express measurements in scientific notation:

1. Identify the decimal point: In the given measurement, 5800m, the decimal point is not explicitly stated. However, it is assumed to be at the end of the number, making it 5800.

2. Determine the coefficient: The coefficient is the non-zero digit(s) at the beginning of the number. In this case, the coefficient is 5.8.

3. Determine the exponent (power of ten): To express the number in scientific notation, you need to find the power of ten that shifts the decimal point to the correct position.

- If you need to shift the decimal point to the left, the exponent is positive.
- If you need to shift the decimal point to the right, the exponent is negative.

In this example, the decimal point needs to move three places to the left from the original position at the end of 5800 to the beginning of 5.8. Therefore, the exponent is 3.

4. Expressing in scientific notation: Now, you can represent the original measurement in scientific notation by combining the coefficient (5.8) and the power of ten (3). The answer is: 5.8 * 10^3.

Remember, the placement of the decimal point determines the value of the exponent, and the power of ten allows for easier representation of large or small numbers.

Understanding and mastering scientific notation can take some practice, but once you get the hang of it, it becomes easier. Let me explain how to express a measurement in scientific notation.

First, let's take the example of expressing 5800m in scientific notation, which is 5.8 * 10^3.

In scientific notation, the general format is a number between 1 and 10, multiplied by 10 raised to some exponent. The exponent tells us how many places to move the decimal point.

To express 5800m in scientific notation, we need to find a number between 1 and 10. In this case, we can see that 5.8 is between 1 and 10.

Now, we need to find out how many places we moved the decimal point to get from 5800 to 5.8. To do that, count the number of decimal places you moved to the left. Here, we moved the decimal point 3 places to the left.

Finally, we combine the number between 1 and 10 (which is 5.8) with 10 raised to the power of the number of places we moved the decimal point (which is 3). This gives us 5.8 * 10^3, which is the scientific notation for 5800m.

To make it easier for you, here are some steps you can follow:

1. Start by identifying the number between 1 and 10 from the given measurement. If the given measurement is not already in that range, move the decimal point until it is.
2. Count the number of places you moved the decimal point.
3. Write down the number between 1 and 10 and multiply it by 10 raised to the power of the count from step 2.

Remember, when expressing a number in scientific notation, the goal is to write it in a simplified form that represents the original measurement while making it more manageable and easier to work with. Practice more examples, and you'll become more comfortable and confident with scientific notation.