Powers of 10: patterns | Place value and decimals | 5th grade | Khan Academy

TL;DR

Multiplying a number by 10 repeatedly follows a pattern where the number of zeros in the answer corresponds to the number of times it was multiplied by 10. This pattern can be represented using exponents.

Transcript

So let's think about what happens when we multiply by 10, and see if we can see some type of a pattern. So let's just start with 1 and multiply that 1 by 10. And this, of course, is equal to 10. You knew that already. But let's multiply by 10 again. So let's do 1 times 10. And now let's multiply by another 10. Let's multiply by another 10. So what'... Read More

Key Insights

• #️⃣ Multiplying a number by 10 repeatedly adds a zero to the end of the number.
• ⚾ Exponents provide a shorthand notation for representing repeated multiplication by the same base.
• ⌛ The exponent represents the number of times the base was multiplied by itself.
• ✖️ The pattern of multiplying by 10 can be easily understood and calculated using exponents.
• 💄 Exponentiation simplifies calculations and makes patterns more apparent.
• 👻 Exponents allow for efficient and concise representation of repeated multiplication.
• ✖️ The base of an exponent represents the number being multiplied, while the exponent represents the number of times it is multiplied.

Questions & Answers

Q: What pattern emerges when multiplying a number by 10 multiple times?

When a number is multiplied by 10, each multiplication adds a zero to the end of the number. The number of zeros corresponds to the number of times it was multiplied by 10.

Q: How can this pattern be represented using exponents?

The pattern can be represented using exponents, where the base is 10 and the exponent represents the number of times 10 was multiplied. For example, 10 multiplied by itself 4 times can be written as 10^4.

Q: How is multiplying by 10 related to exponentiation?

Multiplying a number by 10 multiple times is equivalent to raising 10 to a certain power. The power or exponent represents the number of times 10 was multiplied, while the base remains 10.

Q: What is the result when multiplying 10 by itself 6 times?

Multiplying 10 by itself 6 times, or calculating 10 to the power of 6, results in the number 1 followed by six zeros, which is equal to one million.

Summary & Key Takeaways

• Multiplying a number by 10 follows a pattern where each multiplication adds a zero to the end of the number.

• This pattern can be represented using exponents, where the base is 10 and the exponent represents the number of times 10 was multiplied.

• Using exponents, the pattern becomes clearer and calculations become simpler.