Integer Exponents and Scientific Notation: example 10.74

Write $37,000$ in scientific notation.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write in scientific notation: $96,000 .$

How did it go?

Step 1: Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
Step 2: Count the number of decimal places, $n$ , that the decimal point was moved.	3.70000 4 places
Step 3: Write the number as a product with a power of 10.	$3.7 \times 10^{4}$
If the original number is: greater than 1, the power of 10 will be $10^{n}$ . between 0 and 1, the power of 10 will be $10^{−n}$
Step 4: Check.
$10^{4}$ is 10,000 and 10,000 times 3.7 will be 37,000.
	$37,000 = 3.7 \times 10^{4}$

Step 1: Move the decimal point so that the first factor is greater than or equal to 1 but less than 10.
Step 2: Count the number of decimal places, $n$ , that the decimal point was moved.	3.70000 4 places
Step 3: Write the number as a product with a power of 10.	$3.7 \times 10^{4}$
If the original number is: greater than 1, the power of 10 will be $10^{n}$ . between 0 and 1, the power of 10 will be $10^{−n}$
Step 4: Check.
$10^{4}$ is 10,000 and 10,000 times 3.7 will be 37,000.
	$37,000 = 3.7 \times 10^{4}$