Scientific notation is a way of writing very small or very large numbers in a convenient decimal form by multiplying the number by a power of 10. It is written as a x 10n, where a is between 1 and 10 and n is an integer power of 10. To write a number in scientific notation, the decimal point is moved to place the number between 1 and 10, and the number of places moved is the exponent. The number is then multiplied by 10 to that exponent. Examples are provided of numbers written in scientific notation and vice versa. Rules for significant figures in numbers are also outlined.
QUATER-1-PE-HEALTH-LC2- this is just a sample of unpacked lesson
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.
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.
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
