Dividing Scientific Notation | MathHelp.com - By MathHelp.com
| 00:0-1 | to divide numbers that are written in scientific notation Such | |
| 00:04 | as 6.5 times 10 cubed , divided by 9.8 times | |
| 00:10 | 10 to the 9th . We first divide the decimals | |
| 00:14 | In this case 6.5 divided by 9.8 To get 0.663265306 | |
| 00:25 | . And let's go ahead and round this decimal to | |
| 00:28 | the nearest 100th . Since the three to the right | |
| 00:31 | of the rounding place is less than five . We | |
| 00:34 | round down So we have 0.66 . Next we divide | |
| 00:41 | the powers of 10 . In this case 10 cubed | |
| 00:45 | divided by 10 to the 9th . And since we're | |
| 00:48 | dividing two powers that have like bases , we subtract | |
| 00:52 | the exponents and leave the base the same To get | |
| 00:56 | 10 to the 3 -9 or 10 to the -6 | |
| 01:01 | . So we have 0.66 times 10 to the -6 | |
| 01:07 | . Finally were asked to write our answer in scientific | |
| 01:11 | notation , Notice that our decimal 0.66 is not between | |
| 01:17 | one and 10 . So our number is not in | |
| 01:21 | scientific notation . In this situation we multiply 0.66 by | |
| 01:28 | 10 which moves the decimal .1 place to the right | |
| 01:33 | And we have 6.6 . Now our decimal is between | |
| 01:38 | one and 10 . However , if we multiply the | |
| 01:42 | decimal by 10 Then we must divide the power of | |
| 01:46 | 10 by 10 in order to balance things out . | |
| 01:50 | So we have 10 to the negative six divided by | |
| 01:53 | 10 or 10 to the negative six divided by 10 | |
| 01:57 | to the first , Which means that we subtract the | |
| 02:00 | exponents negative 6 -1 To get -7 . So we | |
| 02:06 | have 6.6 times 10 to the negative 7th , which | |
| 02:10 | is our final answer written in scientific notation . |
DESCRIPTION:
To multiply numbers that are in written in scientific notation, such as 1.4 x 10 to the -2nd times 5.3 times 10 to the 6th, we first multiply the decimals, in this case 1.4 times 5.3, to get 7.42. Next, we multiply the powers of 10, in this case 10 to the -2nd times 10 to the 6th. Notice that weâre multiplying two powers that have like bases, so we add the exponents and leave the base the same, to get 10 to the -2 + 6, or 10 to the 4th. So we have 7.42 times 10 to the 4th. Finally, weâre asked to write our answer in scientific notation. Notice, however, that 7.42 times 10 to the -4th is already written in scientific notation, because we have a decimal between 1 and 10 that is multiplied by a power of 10. So we have our answer.
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