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How to write in Scientific Notation

A positive number is written in scientific notation if it is written in the form:

a x 10y

where 1 < a < 10 and r is an integer power of 10.

Step one: Move the decimal point after the first non-zero number.

Step two: Count the number of decimal places moved in previous step.

-so if you moved the decimal to the left the count is positive.
- if you moved the decimal to the right the count is negative.

Step three: write as a product of the number found in step one and raise it to the power of the number found in step two.

Example 1: write the number in scientific notation.
934,000,000,000

Step 1: move decimal point to where it creates a number between 1-10
934,000,000,000. <-- Decimal is at end of number
9.34 <-- move decimal create number between 1-10

Step 2: count number decimal points moved in step 1
We started at the end of the number 934,000,000,000 and moved it between the 7 and 3. A move of 11 places to the left.
That gives us +11.

Step 3: write as a product of number found in step one and raise it to the power found in step 2.
so we get (the answer is): 9.34 x 10^11 (9.34 x 10 to the positive 11th power.)

Example 2: write the number in scientific notation.
.000026

Step 1: move decimal point to where it creates a number between 1-10
.000026 <-- Decimal is at beginning of number
2.6 <-- move decimal create number between 1-10

Step 2: count number decimal points moved in step 1
We started at the beginning of the number .000026 and moved it between the 1 and 5. A move of 5 places to the right that gives us -5.

Step 3: write as a product of number found in step one and raise it to the power found in step 2.
so our answer is: 2.6 x 10^-5 (2.6 x 10 to the negative 5 power)

And that is how you writer in scientific notation.

Comments

Thanks for the primer Stephanie. The next step is entering the number into the calculator. In your last example the answer was 2.6 x 10^-5. Although we are only dealing with one number a scientific calculator will read this as two numbers to be multiplied. Order of operations will be followed in long sequences. So get use to using the exponential key (EXP, E, EE) on your calculator. It takes the place of x10^.