Our number system is called the base-ten system because it is built on groups of ten. When you count past nine, you run out of single digits. To show ten, you write '10'-a 1 in the tens place and a 0 in the ones place. This place-value system is powerful because it lets us write any number, no matter how large, using only ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Each place in a number is worth ten times the place to its right. The ones place is 1. The tens place is 10 times 1, which is 10. The hundreds place is 10 times 10, which is 100. The thousands place is 10 times 100, which is 1,000. This pattern continues forever. Because each place is ten times the previous one, moving a digit one place to the left multiplies its value by ten. Moving it one place to the right divides its value by ten.
Why is our number system called the 'base-ten' system?
The word multiplies appears in the chunk above. The text says moving a digit one place to the left 'multiplies its value by ten.' If the digit 5 moves from the ones place to the tens place, what happens to its value?
Can you think of other systems that use groups? For example, eggs are sold in dozens. How is a dozen like the base-ten system?
Zero is essential in the base-ten system. Without zero, we would have no way to show an empty place. The number 502 means 5 hundreds, 0 tens, and 2 ones. If we left out the zero, we would have 52, which is a completely different number. The zero holds the tens place so that the 5 stays in the hundreds place. This is why zero is called a placeholder.
Place value also helps us compare numbers. When comparing 4,521 and 4,489, we start with the highest place value. Both numbers have 4 in the thousands place, so we look at the hundreds place. The first number has 5 hundreds and the second has 4 hundreds. Because 5 hundreds is greater than 4 hundreds, we know that 4,521 is greater than 4,489 without checking the rest of the digits. Place value gives us a shortcut for comparing.
Why is zero called a 'placeholder' in the base-ten system?
When comparing 4,521 and 4,489, why do we only need to look at the hundreds place?
Have you ever seen a price like $9.99 instead of $10.00? How does place value make $9.99 seem smaller even though it is almost the same amount?