Powers and Exponents Chapter Notes | Mathematics for Grade 6 PDF Download

Introduction

Exponents are a simple way to show repeated multiplication of a number. For example, in 5³, the exponent 3 means you multiply 5 three times. Powers of 10, like 100 or 0.01, use exponents to represent numbers with zeros or decimal places. The exponent tells you how many zeros or decimal places there are. This guide explains exponents, including positive and negative powers of 10, with clear examples to make them easy to understand.

Exponents

What is an exponent?

• An exponent is a number that shows repeated multiplication.
• For Example: In 5³, the exponent is 3. This tells you to multiply three 5s.
  5³ = 5 × 5 × 5
  In 5³, 3 is the exponent, and 5 is the base.
  

Exponents with powers of 10

• Powers of 10 are numbers like 10, 100, and 1,000. They have a 1 followed by one or more zeros. Powers of 10 can always be written with an exponent.
• Look at the table. Do you see a pattern in the number of zeros and the exponent?
  The exponent matches the number of zeros! You can use that pattern to write powers of 10.
• For Example: How would you write 1,000,000 as a power of 10?
  There are 6 zeros, so the exponent will be 6.
  1,000,000 = 10⁶
  You can go the other direction, too. Let's try it with 10¹². There will be 12 zeros.
  10¹² = 1,000,000,000,000
  That's a trillion!

Powers of 10

What are powers of 10?

• Powers of 10 are numbers like 10, 100, and 1,000. Powers of 10 can always be written with an exponent.
• Look at the table. Do you see a pattern in the number of zeros and the exponent?
  The exponent matches the number of zeros! You can use that pattern to write powers of 10.
• For Example: Let's try it with 1,000,000.
  There are 5 zeros, so the exponent is 5.
  100,000 = 10⁵
  You can use the pattern to evaluate powers of 10, too. Let's try it with 10⁸. There will be 8 zeros.
  10⁸ = 100,000,000
  You can check the answer by using repeated multiplication.

Did you know?

1 is a power of 10? It is 100!

Powers of 10 with negative exponents

• You can also have powers of ten with negative exponents. For example, 0.01 is a power of 10. You can write it as 10^–2.
• You can write a negative exponent as a positive exponent under a numerator of 1. So, 10^–2 is the same as .
• Look at the table. Do you see a pattern in the number of decimal places and the exponent?
  The exponent matches the number of decimal places! You can use that pattern to write powers of 10 with negative exponents.
• For Example: Let's try it with 10^–6.
  The exponent is –6. There will be 6 decimal places.
  10^–6 = 0.000001
  You can use the pattern in the other direction, too. Let's try it with 0.0000001.
  There are 7 decimal places. The exponent will be –7.
  0.0000001 = 10^–7

Tip: Remember, for a positive exponent, count the number of zeros. For a negative exponent, count the number of decimal places.