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Scientific Notation
Scientific Notation is a way of writing very small or very
large numbers in convenient decimal form and multiplied by
a power of 10. It is written in the form of a x 10n
where n is the power of 10 and an integer, and a is a
number whose absolute value is at least 1 but less than 10
(1≤ |𝑎|<10).
To write a number in scientific notation, follow the
following steps.
1. Move the decimal point in the standard form so that the new number
has a value between 1 and 10
2. Count the number of decimal places the decimal point is moved in
Step 1.
• If the decimal point is moved to the left, the sign of the count is
positive.
• If the decimal point is moved to the right, the sign of the count is
negative.
3. Multiply the result in Step 1 by 10 raised to an exponent equal to the
count obtained in Step 2.
Write the following in scientific notation.
1. 65,000,000 = 6.5000000
2. 3,609 = 3.609 x 103
3. 34.6234 = 3.46234 x 101
4. 0.00034 = 00003.4 = 3.4 x 10-4
5. 0.506400 = 05.06400 = 5.064 x 10-1
6. 546.07000 = 5.4607000 = 5.4607 x 102
1. 5.623 x 10 -4
2. 1 x 10 4
3. 4.1 x 10 -2
4. 1.20568 x 5
5. 1 x 10 -10
In writing a scientific form into a decimal or
standard form,
The movement of the decimal point, if the exponent is
negative, is n units to the left.
The movement of the decimal point, if the exponent is
positive, is the n units to the right.
Write the following in decimal notation.
1. 2 x 10-9
2. 3.5 x 104 = 35000 = 35,000
3. 4.056 x 103 = 4056 = 4,056
4. 1.0058 x 106 = 1005800. = 1,005,800
5. 3.21 x 10-5 = .0000321 = 0.0000321
6. 5.004 x 10-2 = .05004 = 0.5004
7. 3.6 x 10-7 = .00000036 = 0.00000036
Rules for Significant Figures
1. All nonzero digits are always significant.
Number Significant Figures
38 792 5
2.157 4
0.2617 4
2. All zeros between nonzero digits are significant.
Number Significant Figures
400.5 5
201.1406 7
0.8003 4
501 3
3. All zeros which are simultaneously to the right of the decimal
point and at the end of the number, are always significant (if and
only if decimal are specified).
Number Significant Figures
2.300 4
56.8000 6
1.00 3
50.0 3
201.03200 8
4. Leading zeros are not significant.
Number Significant Figures
0.0004 1
0.000028 2
0.0629 3
Significant figures and scientific notation

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Significant figures and scientific notation

  • 1.
  • 2. Scientific Notation Scientific Notation is a way of writing very small or very large numbers in convenient decimal form and multiplied by a power of 10. It is written in the form of a x 10n where n is the power of 10 and an integer, and a is a number whose absolute value is at least 1 but less than 10 (1≤ |𝑎|<10).
  • 3. To write a number in scientific notation, follow the following steps. 1. Move the decimal point in the standard form so that the new number has a value between 1 and 10 2. Count the number of decimal places the decimal point is moved in Step 1. • If the decimal point is moved to the left, the sign of the count is positive. • If the decimal point is moved to the right, the sign of the count is negative. 3. Multiply the result in Step 1 by 10 raised to an exponent equal to the count obtained in Step 2.
  • 4. Write the following in scientific notation. 1. 65,000,000 = 6.5000000
  • 5. 2. 3,609 = 3.609 x 103 3. 34.6234 = 3.46234 x 101 4. 0.00034 = 00003.4 = 3.4 x 10-4 5. 0.506400 = 05.06400 = 5.064 x 10-1 6. 546.07000 = 5.4607000 = 5.4607 x 102
  • 6. 1. 5.623 x 10 -4 2. 1 x 10 4 3. 4.1 x 10 -2 4. 1.20568 x 5 5. 1 x 10 -10
  • 7. In writing a scientific form into a decimal or standard form, The movement of the decimal point, if the exponent is negative, is n units to the left. The movement of the decimal point, if the exponent is positive, is the n units to the right.
  • 8. Write the following in decimal notation. 1. 2 x 10-9
  • 9. 2. 3.5 x 104 = 35000 = 35,000 3. 4.056 x 103 = 4056 = 4,056 4. 1.0058 x 106 = 1005800. = 1,005,800 5. 3.21 x 10-5 = .0000321 = 0.0000321 6. 5.004 x 10-2 = .05004 = 0.5004 7. 3.6 x 10-7 = .00000036 = 0.00000036
  • 10. Rules for Significant Figures 1. All nonzero digits are always significant. Number Significant Figures 38 792 5 2.157 4 0.2617 4
  • 11. 2. All zeros between nonzero digits are significant. Number Significant Figures 400.5 5 201.1406 7 0.8003 4 501 3
  • 12. 3. All zeros which are simultaneously to the right of the decimal point and at the end of the number, are always significant (if and only if decimal are specified). Number Significant Figures 2.300 4 56.8000 6 1.00 3 50.0 3 201.03200 8
  • 13. 4. Leading zeros are not significant. Number Significant Figures 0.0004 1 0.000028 2 0.0629 3