Multiplying decimals: place value and reordering | Decimals | Pre-Algebra | Khan Academy

TL;DR

Learn how to multiply decimals by understanding the shifting of decimal places and the division by powers of ten.

Transcript

Let's see if we can calculate 2.91 times 3.2. And I encourage you to pause this video and try it out on your own. So the way I'm going to think about it is 2.91 is the same thing as 291 divided by 10. Or not divided by 10, divided by 100. And we know that if you divide something by 100, you are going to move the decimal place two places to the left... Read More

Key Insights

• 😑 Decimals can be expressed as divisions to simplify calculations.
• ↔️ Shifting the decimal places to the left or right affects the value of a decimal number.
• 👻 Dividing by powers of ten allows for the correct placement of decimal places in the final product.
• 🥇 The number of decimal places in the product is determined by the changes made during the calculations.
• 🪈 The process of multiplying decimals involves re-ordering and dividing to simplify the calculation.
• 🤑 Understanding the concept of decimal multiplication helps in solving real-life problems involving measurements and money.
• 🥇 Multiplying decimals requires attention to detail, especially in properly shifting the decimal places.

Questions & Answers

Q: How can 2.91 be rewritten as a division?

2.91 can be expressed as 291 divided by 100, or moving the decimal two places to the left.

Q: What is the equivalent expression for 3.2 as a division?

3.2 can be written as 32 divided by 10, or moving the decimal one place to the left.

Q: How can we simplify the expression 2.91 times 3.2?

By substituting the divisions, the expression becomes 291 times 32 divided by 100.

Q: Why is dividing by 1,000 significant in this calculation?

Dividing by 1,000 is necessary to shift the decimal places back to their original positions after the multiplication process.

Summary & Key Takeaways

• The video explains how to calculate the product of two decimals, using the example of 2.91 multiplied by 3.2.

• The process involves re-expressing the decimals as divisions, multiplying the numerator, and then dividing by powers of ten.

• The number of decimal places in the product is determined by the changes made during the calculation.