Number of Significant Digits ws 1
Remember These Rules:
1. Digits from 1-9 are always significant – example ______
2. SANDWHICHED Zeros between two other significant digits are always significant – example ______
3. One or more TRAILING zeros to the right of both the decimal place and another significant digit are significant – example ______
4. Trailing zeros in an number without a decimal are placeholders and not significant example ______
5. LEADING zeros are never significant (they are placeholders) example ______
6. Numbers in front of the X sign when written in scientific notation are always significant
Identify the number of significant digits shown in each of the following examples.
1) 400 / 2) 200.0 / 3) 0.0001 / 4) 218
5) 320 / 6) 0.00530 / 7) 22 568 / 8) 4755.50
Answers: 1) 1 2) 4 3) 1 4) 3 5) 2 6) 3 7) 5 8) 6
1) 23.7 x 10-2 / 2) 1.4 x 107 / 3) 4.293 x 104 / 4) 705 / 5) 600
6) 4301.0 / 7) 0.00056 / 8) 40280 / 9) 33214 / 10) 2.003
Answers 1) 3 2) 2 3) 4 4) 3 5) 1 6) 5 7) 2 8) 4 9) 5 10) 4
Honors Chemistry Name______Period___
Scientific notation and sig figs ws 2
Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056,we write 5.6 x 10-9. So, how does this work?
We can think of 5.6 x 10-9 as the product of two numbers: 5.6 (the digit term) and 10-9 (the exponential term).
Here are some examples of scientific notation. Notice the number of sig figs is equal to the number of digits in front of the X sign
problem / Sig figs / Sig figs1. / 1 x 104 = / 9. / 24327 =
2. / 1000 = / 10. / 7354 =
3. / 101 = / 11. / 48200=
4. / 0.01 = / 12. / 0.48200 =
5. / 1/10 = 0.1 = / 13. / 89 = 8.9 x 101 (not usually done)
6. / 1/1000 = 0.001 = / 14. / 0.32 = 3.2 x 10-1 (not usually done)
7. / 0.053 = 5.3 x 10-2 / 15. / 0.0078 = 7.8 x 10-3
8. / 0.0530 = 5.30 x 10-2 / 16. / 0.00044 = 4.4 x 10-4
A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left.
In scientific notation, the digit term indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example,
46600000 = 4.66 x 107
This number only has 3 significant figures. The zeros are not significant; they are only holding a place. As another example,
0.00053 = 5.3 x 10-4
This number has 2 significant figures. The zeros are only place holders.
How to do calculations - On your scientific calculator:
Make sure that the number in scientific notation is put into your calculator correctly.
Read the directions for your particular calculator. For inexpensive scientific calculators:
1. Put the number (the digit number) into your calculator.
2. Push the EE or EXP button. Do NOT use the x (times) button!!
3. Enter the exponent number. Use the +/- button to change its sign.
17. To check yourself, multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x 109.