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### 2003-D: Scientific Notation 3: Moving from Incorrect to Correct Scientific Notation

• Topic Cluster: Pure Mathematics
• Topic: Scientific Notation and Orders of Magnitude
• Objective: Given numbers written as digits multiplied by a power of ten but not in proper scientific notation, put the number into proper scientific notation.
• Content:
• Level: 2

#### BACK to Ladder Scientific Notation and Orders of Magnitude

In two previous pods on scientific notation, you learned to convert to an from scientific notation. In this pod, you will learn to convert between numbers that are neither into proper scientific notation. Often, a number that you look up, especially if you need to convert a number from metric notatation, appears to be in scientific notation, but is actually in improper scientific notation. It is best to convert acccuractely.

A number is in scientific notation only if there is exactly one digit to the left of the decimal, and this digit is not zero!

If there are more than one digit to the left of the decimal point, or if there is one digit to the left of the decimal point, but it is zero, then it is not in scientific notation.

### Questions:

For each number given, state if it is in proper scientific notation or not.

1. $$3.42 \times 10^4$$
2. $$9.23 \times 10^8$$
3. $$0.414 \times 10^5$$
4. $$0.0070 \times 10^1$$
5. $$1.10 \times 10^0$$
6. $$921. \times 10^4$$
7. $$11.38 \times 10^5$$
8. $$6.0 \times 10^9$$
9. $$34.4 \times 10^1$$
10. $$746.2 \times 10^{15}$$
11. $$0.097 \times 10^5$$
12. $$56.7 \times 10^{11}$$
##### Changing from incorrect to correct scientific notation
1. Move the decimal point to the correct location. Count how many places you moved it.
2. If you moved it LEFT, you INCREASE the exponent by the number of steps you took.
If you moved it RIGHT, you DECREASE the exponent by the number of steps you took.
• move decimal LEFT = INCREASE exponent
• move decimal RIGHT = DECREASE exponent

Figure out if the number is in correct scientific notation. If it is not, convert it to corret scientific notation.

1. $$3.42 \times 10^4$$
2. $$9.23 \times 10^8$$
3. $$0.414 \times 10^5$$
4. $$0.0070 \times 10^{-5}$$
5. $$1.10 \times 10^0$$
6. $$921 \times 10^4$$
7. $$11.38 \times 10^5$$
8. $$6.0 \times 10^9$$
9. $$34.4 \times 10^1$$
10. $$746.2 \times 10^{15}$$
11. $$0.097 \times 10^5$$
12. $$56.7 \times 10^{11}$$