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# Writing in scientific notation khan academy

A number is written in scientific notation when there is a number greater than or equal to 1 1 1 1 but less than 1 0 10 1 0 10 multiplied by a power of 1 0 10 1 0 10.

The following numbers are written in scientific notation:

• 5. 4 × 1 0 3 5.4\times 10^3 5. 4 × 1 0 ​ 3 ​ ​ 5, point, 4, times, 10, start superscript, 3, end superscript
• 8. 0 1 3 × 1 0 − 6 8.013\times10^ 8. 0 1 3 × 1 0 ​ − 6 ​ ​ 8, point, 013, times, 10, start superscript, minus, 6, end superscript

## Writing numbers in scientific notation

### Numbers greater than 1 0 10 1 0 10

If we have a number greater than 1 0 10 1 0 10. we move the decimal point to the left until we have a number between 1 1 1 1 and 1 0 10 1 0 10. Then, we count the number of times we moved the decimal and write that as an exponent over a base of 1 0 10 1 0 10. Finally, we write our number multiplied by the power of 1 0 10 1 0 10.

Let's write 6 0 4. 0 0 0 604000 6 0 4. 0 0 0 604, comma, 000 in scientific notation.

If we move the decimal left once, we get 6 0. 4 0 0. 0 60400.0 6 0. 4 0 0. 0 60, comma, 400, point, 0. We need to keep moving the decimal until we get a number between 1 1 1 1 and 1 0 10 1 0 10.

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

Now, we have 6. 0 4 6.04 6. 0 4 6, point, 04.

Finally, we multiply 6. 0 4 6.04 6. 0 4 6, point, 04 times 1 0 5 10^\goldD5 1 0 ​ 5 ​ ​ 10, start superscript, start color goldD, 5, end color goldD, end superscript.

6 0 4. 0 0 0 604000 6 0 4. 0 0 0 604, comma, 000 in scientific notation is 6. 0 4 × 1 0 5 6.04\times10^\goldD5 6. 0 4 × 1 0 ​ 5 ​ ​ 6, point, 04, times, 10, start superscript, start color goldD, 5, end color goldD, end superscript.

### Numbers less than 1 1 1 1

If we have a number less than 1 1 1 1. we move the decimal point to the right until we have a number between 1 1 1 1 and 1 0 10 1 0 10. Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of 1 0 10 1 0 10. Finally, we write our number multiplied by the power of 1 0 10 1 0 10.

Let's write 0. 0 0 5 8 0.0058 0. 0 0 5 8 0, point, 0058 in scientific notation.

If we move the decimal right 3 \greenD3 3 start color greenD, 3, end color greenD times, we get a number between 1 1 1 1 and 1 0 10 1 0 10.

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

Finally, we write 5. 8 5.8 5. 8 5, point, 8 times 1 0 − 3 10^> 1 0 ​ − 3 ​ ​ 10, start superscript, start color greenD, minus, 3, end color greenD, end superscript.

0. 0 0 5 8 0.0058 0. 0 0 5 8 0, point, 0058 in scientific notation is 5. 8 × 1 0 − 3 5.8\times 10^> 5. 8 × 1 0 ​ − 3 ​ ​ 5, point, 8, times, 10, start superscript, start color greenD, minus, 3, end color greenD, end superscript.