Place ValuesWorksheets For This SkillMore SkillsFree Online Tests Trial

Our ancestors were so smart that they figured out that they only needed ten digits to represent countless quantities in the decimal number system. The trick they used was to assign different values to places where they wrote the digits. For example, they did not need a digit to represent quantity twenty-six in the decimal number system because they just wrote 26 for twenty-six. The digit 2(face value) in 26 has a Place Value of ten and the digit 6(face value) in 26 has a Place Value of one. So 26 means 2 tens plus 6 ones, which add up to twenty-six.

It is a convention to assign the lower value to the places on the right and assign the higher values to the places on the left. Let us list the place values from the lowest to the higher:
Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, ......
There are higher place values that are not listed here. But it is not hard to imagine what those higher values are since each place value is 10 times the place value to its immediate right.

Example: show the place values of the digits in number 3,147,895
7895 has 3 in Millions place,
1 in the Hundred Thousands place,
4 in the Ten Thousands place,
7 in the Thousands place,
8 in the Hundreds place,
9 in the Tens place,
5 in the Ones place.

A whole number can only represent a quantity which is a multiple of one. If you are only working with whole numbers, please skip the rest of this section and go on to the next section about rounding or to the applet

To represent a quantity which is a fraction of one, a decimal number is needed. Like the whole number place values, the decimal place values are higher on the left and lower on the right. Let us list the decimal place values from the highest to the lower:
Tenths, Hundredths, Thousandths, Ten-Thousandths, Hundred-Thousandths, Millionths, ......
There are lower place values that are not listed here. But it is not hard to imagine what those lower values are since each place value is one tenth of the place value to its immediate left.

Example: show the place values of the digits in number 3.147895
3.147895 has 3 in Ones place,
1 in the Tenths place,
4 in the Hundredths place,
7 in the Thousandths place,
8 in the Ten-Thousandths place,
9 in the Hundred-Thousandths place,
5 in the Millionths place.

RoundingWorksheets For This SkillMore SkillsFree Online Tests Trial

Sometimes you want to get a rough idea on some quantity because it is too hard to figure out its exact value or the exact value does not matter much. What you need here is estimation. To get an estimation, you often need to approximate the value that a number represents. For example, when you are watching a football game, you wonder how many people are watching with you in the stadium. It is impossible to count everybody in the stadium because there are so many of them. So you just count how many rows there are in the stadium and estimate the number of people on each row. Say, there are approximately 50 rows(the exact number of rows is 49)in the stadium, and there are approximately 100 people(on some rows, there are 94 people, on other rows, there are 108 people) on each row. Then you multiply 50 by 100 to get the total number of people, which is 50,000. This is not the exact number of people who are watching the game, but this number at least gives you an idea about how many people are watching the game.

Rounding is used to approximate the value of a number according to certain rules. To round a whole number, first determine the place to which the number needs to be rounded, let us call it the rounding place. Check the digit to the immediate right of the rounding place: if it is less than 5, replace all the digits to the right of the rounding place with digit 0; if it is equal to or greater than 5, add 1 to the digit in the rounding place and replace all the digits to the right of the rounding place with digit 0.

Example: Round 3,147,895 to the nearest Thousands
The rounding place is the Thousands place. Since the digit in the Hundreds place is 8, which is bigger than 5, add 1 to the digit at the Thousands place, 7, and we get 8. Replace the digits in the Hundreds, Tens and Ones places with 0. Therefore, 3,147,895 rounded to the nearest Thousands is 3,148,000.

If you are only working with whole numbers, please skip the rest of this section and go on to the next section about comparing numbers or to the applet

Rounding a decimal number is not much different from rounding a whole number. The only difference is that you simply drop off all the digits to the right of the rounding place instead of replacing them with digit 0. If the digit in the rounding place is 9, and you need to add 1 to it, then you need to carry 1 over to the next higher place and keep the digit 0 in the rounding place. In other words, a digit should always appear at the rounding place after a decimal number is rounded.

Example: Round 0.39632 to the nearest Thousandths
The rounding place is the Thousandths place. Since the digit in the Ten-Thousandths place is 3, which is less than 5, just drop the digits in the Ten-Thousandths and Hundred-Thousandths place. So 0.39632 rounded to the nearest Thousandths is 0.396 .

Example: Round 0.39632 to the nearest Hundredths
The rounding place is the Hundredths place. Since the digit in the Thousandths place is 6, which is bigger than 5, add 1 to the digit 9 at the Hundredths place and drop the digits in the Thousandths, Ten-Thousandths and Hundred-Thousandths place. Since 9 plus 1 is 10, we carry 1 over to the Tenths place and 3 plus 1 yields 4 in the Tenths place. Remember to keep the digit 0 in the Hundredths place, so 0.39632 rounded to the nearest Hundredths is 0.40 .

Comparing Whole Numbers or DecimalsWorksheets For This SkillMore SkillsFree Online Tests Trial

First of all, you should be able to compare single digit numbers:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9

To compare multi-digit whole numbers, first check whose highest place value is higher. The number with the higher highest place value is bigger. If the numbers have the same highest place value, then compare the digits with the highest place value. The number with a bigger digit in the highest place is bigger. If the digits with the highest place value are the same, then compare the digits with the next highest place value. Continue this process until two different digits are found in the same place or the Ones place is reached. Obviously, if the numbers have the same digits in every place, then the numbers are equal.

Example: Which one is bigger, 3,147,895 or 999,999?
The highest place value for 3,147,895 is Millions, while the highest place value for 999,999 is Hundred Thousands, so 3,147,895 is bigger than 999,999.

Example: Which one is bigger, 6592 or 6589?
The highest place values for 6592 and 6589 are the same : Thousands, and the digits in the Thousands place are also the same : 6. So we go on to the Hundreds place and find out that the digits in the Hundreds place are also the same : 5 . Then we go on to the Tens place and find out 6592 has a bigger digit in the Tens place than 6589 has in the Tens place since 9 is bigger than 8 . We conclude that 6592 is bigger than 6589 .

There is an important fact about equality and inequality that you should know. The fact is the following:
If a number X is equal to a number Y , and Y is equal to another number Z , then X is equal to Z .
If a number X is greater than a number Y , and Y is greater than another number Z , then X is greater than Z .
If a number X is less than a number Y , and Y is less than another number Z , then X is less than Z .
This fact is called the Transitional Rule of equality and inequality.

If you are only working with whole numbers, please skip the rest of this section and go on to the applet.

To compare decimal numbers, follow the same procedure used to compare whole numbers until two different digits are found in the same place or the end of either decimal number is reached. Just one more thing : If two decimal numbers have the same digit in every place in which they both hold digits, and one decimal number has less decimal places than the other one, then the decimal number with more digits is bigger.

Example: Which one is bigger, 0.6592 or 0.659?
Since 0.6592 and 0.659 have the same digits in the Tenths, Hundredths and Thousandths places, but 0.6592 has 2 in the Ten-Thousandths place , while 0.659 has no digit in the Ten-Thousandths, so 0.6592 is bigger than 0.659 .

Instructions for This AppletFree Online Tests Trial

  1. Click a radio button according to the type of your problem.
  2. Click the check box labeled "Allow Decimals" only if you work on decimal numbers.
  3. Click the first button to print worksheets; click the second button for the applet to ask you a question; click the third button to input your own question.
  4. Hit the space bar when you finish entering a number and want to enter a new one.
  5. Click the "Help" button to see each step when solving your problem.
  6. Type your answer to questions asked by the applet when solving your problem. Just click the "Help" button if you do not want to answer those questions.
  7. If you want to type something on the question bar or the help panel after losing focus on them, click the question bar or the help panel before typing.
  8. Click the "Start Over" button to start over.

Support

Agape Way

Instructions for This AppletHit the F11 key to see this applet on full screen