Now let's say that each of those 1,620 passengers pays $100 for their flight. This means that 10 times 162 is 1,620, and the airline has 1,620 total seats.
Since we have no digit in the ones place, we put a zero there. Following this pattern, the 1 is now in the thousands place, the 6 is in the hundreds place, and the 2 is in the tens place. How many seats is that in total? When you multiply a number by 10, also represented as 10 1, all of the digits in that number shift one place to the left. Let's say that an airline has ten airplanes and each plane has 162 seats. Now let's explore how powers of 10 can help us multiply large numbers. Try this one yourself: What are the three different ways to express one hundred dollars? We can write numbers in three different ways: in standard form (1,000), expanded form (10 × 10 × 10), and exponential form (103). $1,000,000 can be represented as 10 to the power of 6 or 106. $100,000 can be represented as 10 to the power of 5 or 105. $10,000 can be represented as 10 to the power of 4 or 104. $1,000 can be represented as 10 to the power of 3 or 103. The next pile of $100 can be represented as 10 to the power of 2, or 102, since 100 = 10 × 10, or two 10s multiplied together. Our first pile of bills-which was $10-can be represented as 10 to the power of 1, or 101. When working with large numbers, it is sometimes more convenient to represent these numbers in another form, called powers of 10. Each time we multiply by 10, the digits in our number shift one place value to the left. Each new pile has ten times as many dollar bills as the last pile, so our next pile has 10 × 10 × 10 × 10 dollar bills, or $10,000, and the next pile has 10 × 10 × 10 × 10 × 10 bills, which is $100,000. The next pile has 10 × 10 × 10 dollar bills, or $1,000. Next, make another pile with ten times as many dollar bills or 10 × 10 dollars, which is $100. Start by making a pile with ten one-dollar bills, which represents $10. Suitcase of Money Let's say we want to represent a million dollars using powers of 10. We can write numbers in three different ways: in standard form (1,000), expanded form (10 × 10 × 10), and exponential form (10 3). $1,000,000 can be represented as 10 to the power of 6 or 10 6. $100,000 can be represented as 10 to the power of 5 or 10 5.
$10,000 can be represented as 10 to the power of 4 or 10 4. $1,000 can be represented as 10 to the power of 3 or 10 3. The next pile of $100 can be represented as 10 to the power of 2, or 10 2, since 100 = 10 × 10, or two 10s multiplied together. Our first pile of bills-which was $10-can be represented as 10 to the power of 1, or 10 1.
Let's say we want to represent a million dollars using powers of 10.