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Name: _________________________________________________________ Period: ______ Date: ___________________________
11th Grade Mathematics PSSA Preparation Program
Mastered On: _____________________
Scientific Notation
Anchors Addressed
M11.A.1.1.2 – Express numbers and/or simplify expressions using scientific notation (including numbers less
than 1.)
Concepts
Scientific Notation is a method in which numbers, regardless of how large or small, can be efficiently written
using powers of ten. Numbers written in scientific notation consist of two factors: 10 , where a is a
number between 1 and 10, but not 10, and n is the power of ten.
Converting Numbers into Scientific Notation
STEP 1: Move the decimal place so that it is to the right of the first non-zero digit. (So the value of the number
is between 1 and 10. The number can be 1 but not 10.
STEP 2: Count the number of places (n) the decimal point moved and which direction.
STEP 3: If the decimal point moved to the left, write as: 10 . If the decimal moved to the right, write as:
10 .
Example 1: Write 12,723,923 in scientific notation.
Solution: Move the decimal point to the left until the number is between 1 and 10 as shown:
1.2723923 Now, count the number of places the decimal point moved. This number
(7) is your exponent, therefore 12,723,923 written in scientific notation is:
1.2723923 10
Example 2: Write 0.00473562 in scientific notation.
Solution: Move the decimal point to the right until the number is between 1 and 10 as shown:
4.73562 Now, count the number of places the decimal point moved. This number
is your exponent, therefore 0.00473562 written in scientific notation is:
4.73562 10
Calculator Tip: Most scientific calculators will convert number to and from scientific notation.
Many calculators use EE to represent 10 . Therefore, if you wanted to enter 2.3 10 into the
calculator, type /80%C1.
Converting a Number from Scientific Notation
STEP 1: Write the value of a.
STEP 2: If n is negative, add − 1 zeros and a decimal point before the value of a. If n is positive, count the
number of places after the decimal point in a, then add zeros until the number of places after the
decimal point is n. Finally, erase the decimal point from the middle of a from STEP 1.
Example 3: Write 3.14 10
Solution: First write the value of a: 3.14. Since n is positive and there are two digits after the
decimal places, add three zeros to the end and remove the decimal point from between
the 3 and 1, therefore: 3.14 10 is 314,000.
Example 4: Write 2.4 10
Solution: First write the value of a: 2.4. Since n is −4, add three zeros before the 2 and move the
decimal point to the left of the zeros. Therefore, 2.4 10 is 0.00024.
Exercises
A. Convert the following numbers into scientific notation.
1. 7,475,000
3. 0.0002458
5. 1,010
2. 0.0547
4. 302
6. 0.000014
The following exercises work the same way as above, but may look different. Some numbers are written in a
manner similar to scientific notation, but need adjusted because the value of a is not between 1 and 10. In
these cases, if you make the value of a smaller, then you need to make the value of n larger. Conversely, if you
make the value of a larger, then you need to make the value of n smaller. Consider the example below:
Example 5: Convert 42.5 10 into scientific notation.
Solution: Since 42.5 is larger than 10, moving the decimal point one place to the left makes the
value of a smaller by one place. Therefore, increasing n by one place yields: 4.25 10 .
9. 42
11. 1.4
13. 37.8 10
10. 0.58 10
12. 356.2 10
14. 56.24 10
B. Convert the following numbers to standard notation.
15. 3.02 10
17. 7.6 10
19. 1.2574 10
16. 5.4 10
18. 8.56 10
20. 5.4 10
C. Answer the following questions.
21. On August 25, 2011, the U.S. national debt was $14,648,835,000,000, of which $3,654,861,000 was the
total interest paid to lenders in 2011. Write the national debt and the interest paid in 2011 in scientific
notation.
22. Using the debt figure from question 21, if each citizen were to pay his/her share of the debt, how many
citizens are there in the United States if each person is responsible for $46,941?
23. Many monuments in Washington D.C. were built out of marble, a very heavy stone mined in the United
States. Convert the following statistics about monuments in standard notation.
A. Lincoln Memorial weighs 7.6 10 pounds.
B. Tomb of the Unknown Soldier weighs 1.58 10 pounds.
C. Washington Monument weighs 9.0854 10 tons and was built using marble, granite, and limestone.
24. Compare the weights of the monuments from question 23. List the weights from least to greatest on the
lines below. (Recall that 1 ton is 2,000 pounds.)
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