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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

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*Maria Airth*

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Working with decimals can feel daunting, but it doesn't have to be that way. In this lesson, we will learn how rounding, ordering and zeros work with those numbers that are to the right of the decimal point.

**Decimal numbers** are *parts of a whole, or one*. The name of the place value tells you have many you need to make a whole. For example: you need 10 tenths to make a whole.

As a quick review, remember that the decimal number place value names match the whole number names as they move away from the *Ones* place. Moving from the decimal to the right you have the *Tenths*, *Hundredths*, *Thousandths*, etc. This lesson will cover rounding, ordering and dealing with zeros when working with decimals. For further review of decimal place values, take a look at our lesson on What is a Decimal Place Value.

Rounding decimal numbers works exactly the same as rounding whole numbers. The key is to look at the number directly to the right of the place value to which you are rounding. If that number is 5 or greater, you round the target value up. If that number is less than 5, the target number stays the same. Regardless if the number rounds up or stays the same, all the numbers to the right of the target number will change to zero. Let's take a look at how this works.

Round 4354.627 to the nearest *Tens* place.

The number directly to the right of the *Tens* place is a 4. Since it is less than 5, the *Tens* place number does not change and all the numbers to the right change to zeros.

The answer is 4350.000

We can also write this as 4350, leaving off all the extra zeros after the decimal.

Round 4354.627 to the nearest *Hundredths* place.

The number immediately to the right of the *Hundredths* place is a 7 which is greater than 5, so the target value will round up and all the numbers to the right of the target value will change to zeros.

The answer is 4354.630 or 4354.63 (as we can also drop this ending zero).

As you can see, the process for rounding decimal numbers is exactly the same as for rounding whole numbers. All the numbers to the left of the target remain the same, while only the target place value and numbers to the right are impacted by rounding.

Did you notice that we could drop some zeros when rounding? Zeros do not always give essential information and can be left off of some numbers. Any **ending zeros**, zeros at the end of a number, that are in the decimal portion of a number (meaning they are to the right of the decimal) can be dropped because they give no additional information - they are only changing the place value of the number, not the actual value. For example: 64.5000 can be written 64.5.

**Leading zeros**, zeros that start a number, to the left of the decimal (meaning in the whole number part of a number) can be dropped as well. For example: 03.65 can be written 3.65.

The number 0.50 can be written as .5 without changing the value.

The only time you would want to keep zeros is when dealing with money. Monetary amounts require two place values after the decimal to indicate cents to the *Hundredth* place. Writing .5 cents is not appropriate; it should be $0.50.

Just like with rounding, the ordering of decimal numbers works the same as the ordering of whole numbers. When ordering numbers, we look to the left most place value (the largest) to begin, and then continue moving to the right, comparing numbers, until all numbers are ordered. Let's look at a whole number example.

Let's order the following numbers: 134, 123, and 145.

Beginning at the largest place value, we see that all the numbers have a 1 in the *Hundreds* place, so we must look to the next smaller place value to find differentiation between them. Here, we see all the *Tens* places are different, so we can order based on *Tens* values: 123, 134, and 145.

Decimals work similarly in that numbers get larger as they move to the left. Just remember, as you move left in any number, the place values are getting larger by a factor of ten each time; as you move right, the place values are getting smaller by a factor of ten each time.

Let's put these decimal numbers in order from smallest to largest:

0.123, 0.103, and 0.113

Starting at the largest place value (the *Tenths*), we see that they all have a 1 in the *Tenths* place, so we move to the next smaller place value, the *Hundredths* place. Here, they all differ, so this is the place where we can order the digits. Since we only need to look at the *Hundredths* place to order these numbers, we see that the number with a 0 will go first, then the 1, then to 2 so we get: 0.103, 0.113, and 0.123.

Again, lets put these in order from smallest to largest:

123.45, 123.567, and 123.2

Again, we start with the largest place value and work our way to the right. In this example, our whole number of 123 is the same, so we must move onto the decimal part of the number.

Don't let the fact that there are varying digits in the decimal portion confuse you. As you just saw, zeros can be added to the end of decimal numbers without changing the value. So, we will add zeros to make all the numbers have the same amount of digits:

123.450

123.567

123.200

Now we just apply what we have already learned. Starting from the *Tenths* place, we see that the 2 is smaller than the 4 which, in turn, is smaller than the 5. So, these numbers in order from smallest to largest is: 123.2, 123.45, and 123.567.

Place values run in factors of ten getting larger as you move left and smaller as you move right from the *Ones* place (directly to the left of the decimal).

**Decimal** place values indicate how many parts are needed to make 1 whole.

Rounding in decimals works identically to rounding with whole numbers: if the number immediately to the right of the target is 5 or more, round up by making the target value one greater and then change the rest of the numbers to the right of the target to zero; otherwise, round down by keeping the target number the same and changing the numbers to the right to zero.

**Leading zeros** to the left of the decimal can be dropped (0.5 = .5).

**Ending zeros** to the right of the decimal can be dropped (34.50 = 34.5).

When ordering decimals, remember that place values are larger as you move to the left. Find the left most place values that differ between the numbers and order based on comparing digits.

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GED Math: Quantitative, Arithmetic & Algebraic Problem Solving9 chapters | 66 lessons

- Decimal Basics: Rounding, Ordering & Zeros
- What is a Fraction? - Definition and Types 6:20
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Raise and Reduce Fractions 6:17
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Changing Between Decimals and Fractions 7:17
- Using the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46
- Go to GED Math: Decimals & Fractions

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