Scientific notation review

A number is written in scientific notation when there is a number greater than or equal to $1$1 but less than $10$10 multiplied by a power of $10$10.

The following numbers are written in scientific notation:

If we have a number greater than $10$10, we move the decimal point to the left until we have a number between $1$1 and $10$10. Then, we count the number of times we moved the decimal and write that as an exponent over a base of $10$10. Finally, we write our number multiplied by the power of $10$10.

Let's write $604{,}000$604, comma, 000 in scientific notation.

If we move the decimal left once, we get $60{,}400.0$60, comma, 400, point, 0. We need to keep moving the decimal until we get a number between $1$1 and $10$10.

We have to move the decimal left a total $\goldD5$start color #e07d10, 5, end color #e07d10 times.

Now, we have $6.04$6, point, 04.

Finally, we multiply $6.04$6, point, 04 times $10^\goldD5$10, start superscript, start color #e07d10, 5, end color #e07d10, end superscript:

$604{,}000$604, comma, 000 in scientific notation is $6.04\times10^\goldD5$6, point, 04, times, 10, start superscript, start color #e07d10, 5, end color #e07d10, end superscript.

If we have a number less than $1$1, we move the decimal point to the right until we have a number between $1$1 and $10$10. Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of $10$10. Finally, we write our number multiplied by the power of $10$10.

Let's write $0.0058$0, point, 0058 in scientific notation.

If we move the decimal right $\greenD3$start color #1fab54, 3, end color #1fab54 times, we get a number between $1$1 and $10$10.

Now, we have $5.8$5, point, 8.

Finally, we write $5.8$5, point, 8 times $10^{\greenD{-3}}$10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript:

$0.0058$0, point, 0058 in scientific notation is $5.8\times 10^{\greenD{-3}}$5, point, 8, times, 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript.