Exponents and powers of zero patterns | Pre-Algebra | Khan Academy

TL;DR

Powers of 10 are calculated by multiplying 1 by 10 multiple times. Moving the decimal point to the right increases the number, while moving it to the left decreases the number.

Transcript

We are asked what is 10 to the fifth power equivalent to. Well, 10 to the fifth power is the same thing as taking a 1 and multiplying it by 10 five times. So let's do that. So that's three, four, and five. So it's 1 times 10 times 10 times 10 times 10 times 10. Notice one, two, three, four, five. And what's this going to be? Well, 1 times 10 is 10.... Read More

Key Insights

• ✊ Powers of 10 can be found by multiplying 1 by 10 multiple times.
• 🪜 Multiplying a number by 10 increases its value and adds zeros to the product.
• 🗂️ Dividing a number by 10 decreases its value and eliminates zeros from the quotient.
• 😥 The location of the decimal point determines the scale and magnitude of a number.
• ✊ Understanding powers of 10 is fundamental in various mathematical operations and scientific applications.
• 😥 The concept of moving the decimal point helps visualize the impact of multiplying or dividing by powers of 10.
• 😑 Powers of 10 are used to express very large or very small numbers in a concise and convenient way.

Questions & Answers

Q: What is 10 to the fifth power equal to?

10 to the fifth power is equal to 100,000. This can be calculated by multiplying 1 by 10 five times or by adding five zeros to 1.

Q: How many zeros does the product 67 times 10 to the fifth have?

The product of 67 times 10 to the fifth has five zeros. This is because every time you multiply by 10, you add a zero. Therefore, multiplying by 10 five times results in five additional zeros.

Q: How many zeros does the quotient 5,700,000 divided by 10 to the third power have?

The quotient of 5,700,000 divided by 10 to the third power has three zeros. This is because dividing by 10 three times eliminates three zeros from the original number.

Q: When 72.1 is multiplied by 10 to the third, how does the decimal point move?

When 72.1 is multiplied by 10 to the third, the decimal point moves three places to the right. This results in a larger number, 72,100.

Q: When 56 is divided by 10 to the third, how does the decimal point move?

When 56 is divided by 10 to the third, the decimal point moves three places to the left. This results in a smaller number, 0.056.

Summary & Key Takeaways

• To find 10 to the fifth power, multiply 1 by 10 five times, resulting in 100,000.

• When multiplying a number by 10 to the fifth power, you add five zeros to the product.

• Dividing a number by 10 to the third power is the same as dividing by 1,000, resulting in the elimination of three zeros.