Scientific Notation Problems and Insignificant Digits:
Write the numbers below in scientific notation:
1. 345,998,000,000 =
2. 584,345,000,000,000,000 =
3. 0.000000987 =
4. 0.12 =
5. 0.000000000000000000000000000000002 =
6. 23.87 =
7. 273,456,999,000.000098 =
8. 0.0000008760000032 =
9. -789.000 =
10. 1 =
11. 10 =
12. -1 =
Insignificant Digits - did you include the digits after the hundredths place in your answers
above? You don't need to! Here is another important rule for this class. When writing in
scientific notation, you don’t have to write any digits after the hundredths place which is more
than 2 decimal places to the right of where you put the decimal point. For example:
234,876,987,765 = 2.34 x 1011 and 0.000978000023 = 9.78 x 10-4 Why? Unless you have to be
very precise, the digit 3 places to the right of the decimal is 0.001 (one thousandth) of the
number. And every digit after that is 10 times less the value of the previous digit. The digits
more than 2 places to the right of the decimal point are called insignificant digits. Think of a
pie. If I gave you 0.001 piece of the pie it would be insignificant and you would feel cheated! Or
removing a few grains of sand from a beach is insignificant when the whole of all the sand on the
beach is considered. Obviously a few grains from a beach are much less than 0.001 part of the
beach by the way! Here's one more important point. When scientists are measuring things
sometimes they do have to include digits in the number less than 0.001. It depends what they are
measuring. If you need to be extremely precise then all the digits may be significant! If you are
looking for 1 part in a million then a number is significant out to 0.000001.
Write the numbers below in scientific notation and include only the significant digits and
then multiply each number by 2. Remember to adjust the digits correctly in your answers.
13. 678,234,543,000 =
14. - 987,234,567,789,987 =
15. 0.0000000786509008 =
16. 0.000000346000087654007611 =
17. 234, 765, 987, 000, 000, 000, 000.18 =
18. 0.12 =
19. - 0.000034000000679 =
20. 345,987,908,000,000,003 =
21. 87,345,908.0098 =