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### 2003-C: Scientific Notation 2: Standard to Scientific Notation

• Topic Cluster: Pure Mathematics
• Topic: Scientific Notation and Orders of Magnitude
• Objective: Convert numbers from standard notation to scientific notation.
• Content:
• Level: 1

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

In the previous pod, we converted values from scientific notation into the more well known standard notation. In this pod, we will complete the same operation in reverse.

• Step 0: If there is no decimal point, put one at the end of the number.
• Step 1: Move the decimal point until it is in the correct location. It is in the correct location when there is precisely one non-zero digit to the left of the decimal point. Count how many times you moved it.
• Step 2: Figure out if the order of magnitude is positive or negative.
• If you started with a BIG NUMBER and moved the decimal point to the LEFT, then the order of magnitude is POSITIVE.
• If you started with a SMALL NUMBER and moved the decimal point to the RIGHT, then the order of magnitude is NEGATIVE
• If you didn't need to move the exponent at all, then the order of magnitude is zero.
• BIG NUMBER = move LEFT = POSITIVE exponent
LITTLE NUMBER = move RIGHT = NEGATIVE exponent
• Add the order of magnitude. It is equal to the number of times you moved the decimal, and is positive or negative.

Make sure that that you place the decimal point correctly for scientific notation!

#### Questions:

For each number, convert from standard notation to proper scientific notation.

1. $$3420000$$
2. $$32400$$
3. $$5830000000$$
4. $$1230$$
5. $$14$$
6. $$9$$
7. $$0.00000123$$
8. $$0.000145$$
9. $$0.000000000123$$
10. $$0.0000001241$$
11. $$11240000$$
12. $$81$$
13. $$7$$
14. $$990000$$
15. $$0.141$$
16. $$0.0132$$

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

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