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Zeros
Let me make a comment about zeros. Zeros came up when we were dealing with significant
digits earlier. When changing a number to scientific notation, drop any zeros which are
used just to hold the decimal place, but keep any zeros which are significant digits. All
zeros shown in scientific notation should be significant digits because the exponent,
rather than the decimal place, does the job of letting you know how large or small the
number is.
Here are some examples of zeros that are lost and kept.
| In the number 0.04500 the first zero is lost when changed to scientific
notation but the two zeros at the end are kept. |
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| In this example, we have no indication that any of the zeros have been
measured as significant digits. Therefore, we presume that they were all serving as
decimal placeholders and write the number as 3.7 times 10 to the fifth. |
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| In this example, the plus or minus 1,000 tells you how many of those
digits were actually measured. The last three zeros are just place holders, but the zero
in the 1,000 place must have been measured (because we know the number to the nearest
1,000). That zero is kept; but the other zeros, which are only holding the decimal place,
are lost when you move the decimal place to put the number into scientific notation. |
| 370,000 (±1000) = 3.70 x 105
^
it is known that this zero is a significant digit because
of the "±1000"
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