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Scientific notation sounds may sound scary, but it’s really not. It’s actually very easy! In this lesson, you’ll learn how to write 1000 in scientific notation in a step by step fashion.

Steps To Solve

Background Information

If you’ve ever wanted to simplify a really big number into something much easier read, you’d use scientific notation. Scientific notation is the shorthand writing method for numbers in math. To use scientific notation, you’d write a number in the following format:A x 10bHere’s what all those letters stand for:

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  • A is called the coefficient.

    The coefficient is always greater than or equal to 1 but less than 10.

  • ‘x’ is the multiplication sign. You knew that!
  • 10 is known as the base (and it’s always 10 when using scientific notation).

  • b is just the exponent. Perhaps you’ve heard of it alternatively as ‘the power of 10’.

Steps

Knowing this, let’s see how 1000 is written in scientific notation.

Step 1. Since 1000 doesn’t have a decimal point anywhere, place a decimal point at the end of 1000 to make it read ‘1000.’ This will make it easier to follow the additional steps outlined herein.Step 2. Move this number’s (‘1000.’) decimal point to the very right of the first non-zero digit in the number.

In this instance, it’s super easy. The only non-zero digit in 1000 is ‘1’. Following step 2’s instruction, ‘1000’ turns into ‘1.000’.

Step 3. Count how many places you had to move that decimal point. If you think three, you’re right! That’s the exponent, ‘3’. But you must also consider the direction you moved the decimal point. When any decimal point is moved to the left, the exponent is always positive. Since it was moved three places and it was moved to the left, the exponent is +3 or simply 3.

Step 4. To get your coefficient, drop any zeroes that are located before the first non-zero digit and after the last non-zero digit of step 2’s answer of ‘1.000’. There are no zeroes to the left of ‘1.

000′ and there are three zeroes to the right of ‘1.000’. Thus, we drop all those zeroes to the right and we are left with ‘1’, our coefficient.And, that’s it! You now have everything you need to write 1000 in scientific notation:

  • A, the coefficient, is ‘1’ in our case.
  • ‘x’ is the multiplication sign.

    This never changes.

  • 10 is the base and this never changes either.
  • b is the exponent and step 3 told us it is ‘3’ in our case.

Now, all we have to do is fill in the information for A x 10b to get our answer! Doing so, we get:1 x 103

Solution

Writing 1000 in scientific notation isn’t difficult at all.

It is written as 1 x 103.You might be tempted to write 1000 as 103, and mathematically you would be correct since 1 x 103 = 103. However, 103 isn’t in scientific notation because the coefficient is missing. The coefficient is important in science because the number of significant digits in the coefficient signifies the precision of the number.

Application

Scientific notation is used in science all of the time. For example, let’s say you wanted to calculate how many protons are in the sun! You are told that the sun’s mass is 1.98 x 1033 grams. You are also told each proton has a mass of 1.

6 x 10-24 grams.When dividing numbers with exponents, simply subtract the bottom number’s exponent from the top number’s exponent to get your answer’s exponent.To find out how many protons are in the sun you would simply divide the first number by the second like so:( 1.98 x 1033)/( 1.6 x 10-24)To get your answer of 1.2 x 1057 protons.

Working with scientific notation is much simpler than having to write out all those additional zeros for each number. It would be way too messy to do that.

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