Learning Library

# Nine: The Biggest Little Number

Medium

Minimal

None

Common

### Objective

To show and explore how exponents are used.

### Materials

• Paper
• Calculator that can handle large exponents

### Introduction

Mathematicians and scientists use exponents to make their math easier. Big numbers, or very little numbers, can be written more easily using exponents. For example, 400,000,000,000,000,000,000,000 can be written as 4 x 1023, which means 4 with 23 zeroes after it.

99, which is read “9 to the 9th power,” means 9x9x9x9x9x9x9x9x9. With the third superscript, that resulting number is multiplied times itself 9 times. So, in a very tiny space, a very large number is represented.

Learning how exponents work is important for more advanced math such as algebra, trigonometry and calculus, and is essential for sciences such as chemistry and astronomy.

Show the math.

### Research Questions

• What is a positive exponent?
• What is a negative exponent?
• What is a superscript?
• How do scientists use exponents in their work?

### Terms

• Squared: a number times itself, used, among other things, to calculate area
• Cubed: a number time itself, times itself, used, among other things, to calculate volume

### Concepts

Exponents are a method to handle extremely large or extremely small numbers. The distance between stars and galaxies would be difficult to write out even with miles, kilometers or light years. Exponents make this possible. The same is true of dealing with the diameter of an atom, or the wavelength of the color red. Exponents allow scientists to perform needed mathematical functions with these extremely large or extremely small numbers.

### Experimental Procedure

1. To grasp the idea, use paper to manually calculate 9x9x9x9x9x9x9x9x9.
2. Repeat this with a calculator capable of displaying exponents.

### Bibliography

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