10 is related to place value in our base-10 number system. In our base-10 system, each place value represents a power of 10. The ones place represents 10^0, the tens place represents 10^1, the hundreds place represents 10^2, and so on. This place value system allows us to easily compare and order numbers based on their value in each place.

1. How is 10 related to a place
value?
PLACE VALUE
We use a number system called the “base ten”. This means that place value in
any number is based on a pattern of tens.
Look at the following place-value models for whole numbers through thousands.
Thousands Hundreds Tens Ones
1 thousand is 10
times 1 hundred
1 hundred is 10
times 1 ten
1 ten is 10 times 1
one
1,000 + 100 + 10 + 1

2. Look at the pattern in the chart
*Each time the digit 1 moves one place to the left, it is worth ten times more. Each
time the digit move one place to the right, it is worth only one tenth as much.
Comparing Numbers
We can use the place value table to compare numbers.
Look at the number 3,412 and 4,123. Which number is greater?
Thousands Hundreds Tens Ones
3 4 1 2
10 ones make one ten
10 tens make 100
10 hundreds make a 1,000
10 one thousands make 10,000
10 ten thousands make 100,000
10 one hundred thousand make 1,000,000
1
10
100
1,000
10,000
100,000
1,000,000

3. Thousands Hundreds Tens Ones
4 1 2 3
First we compare the thousands. 4 thousand is greater than 3 thousand. So 4,123 is
greater than 3,412.
We use inequality symbols such as > and <.
4,123 > 3,412
Ordering Numbers
We can also order numbers using the place value table.
Thousands Hundreds Tens Ones
5 1 4 2
Thousands Hundreds Tens Ones
3 7 9 8
Thousands Hundreds Tens Ones
5 2 7 6
3 thousands < 5 thousands
3,798 is smaller than 5,142 and 5,276.
So 3,798 is the smallest number.
5,142
3,798
5,276

4. Now we compare 5,142 and ,5276 to see which is greater.
2 hundreds is > 1 hundred.
5,142 > 5,276
So 5,276 is the greater number.
Since 5,376 is also greater than 3,789, 5,276 is the greatest number.
Rounding Off Numbers
We can use a number line to check where a number is closer to.
Rounding off to the nearest ten:
82 is between 80 and 90.
It is nearer to 80 than 90.
82 is 80 when rounded to the nearest ten.
Rounding off to the nearest hundred:
223 is between 200 and 300
It is nearer to 200 than 300.
So 223 is 200 when rounded to the nearest hundred
80
82
200 300250
223
90

5. You can also round numbers following this rule:
Look to the right of the rounding digit. If the digit is from 1-4, round down and change
the rest of the digits to zero. If the digit is from 5-9, round up and change the rest of
the digits to zero.
Look at this example.
14,632 rounded to the nearest ten thousand
14, 632 – 1 is in the ten thousand and the digit that follows is 4
14,632 is 10,000 when rounded to the nearest ten thousand.
176,002 rounded to the nearest hundred thousand
176,002 – 1 is in the hundred thousand place and the digit that follows is 7
176,002 is 200,000 when rounded to the nearest hundred thousand