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### 2003-B: Scientific Notation 1: Scientific to Standard Notation

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

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

In science, we typically represent numbers in a form called scientific notation. In scientific notation, numbers have two parts: the significant figures and the order of magnitude. In the following example, the significant figures are 3.45 and the order of magnitude is +6.

Sometimes, the significant figures are referred to as the coefficient and the order of magnitude is referred to as the exponent. In this class, I prefer to use the term "significant figures" and "order of magnitude."

All of the numbers you are used to writing, such as 10, 28, 415891, are called numbers in standard notation.

• There are multiple ways of writing a number in scientific notation.
• Most typically, it is written as significant digits multiplied by a power of ten:
$$3.45 \cdot 10^{6}$$
• However, scientific notation can also be written with a capital "E":
3.45E6
• It can be written with a lower case "e".
3.45e6
• Lastly, it can be written with a small font size capital "E". I personally find this notation easiest to read.
3.45E6
##### Converting Scientific Notation to Standard Notation
• Rule 1:
• Move the decimal point to the RIGHT if the exponent is POSITIVE.
• Move the decimal point to the LEFT if the exponent is NEGATIVE.
• Move the decimal point as many spots as the exponent.
• Rule 2: After moving the decimal, add zeroes in any empty spots.

### Questions:

Convert each number to standard notation.

1. $$3.45 \times 10^4 =$$
2. $$4.23 \times 10^7 =$$
3. $$9.12 \times 10^2 =$$
4. $$4.87 \times 10^5 =$$
5. $$8.25 \times 10^6 =$$
6. $$2.45 \times 10^0 =$$
7. $$2.45 \times 10^1 =$$
8. $$3.89 \times 10^0 =$$
9. $$4.23 \times 10^{-3} =$$
10. 3.28E-8
11. 6.78E-5
12. 3.85e-4
13. 5.28e-7
14. 3.42E5
15. 4.23E2
16. What do we call the digits at the beginning of a scientific notation number?
17. What do we call the exponent in a scientific notation number?

### Answers:

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

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