UNDERSTANDING DECIMALS
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Decimals are similar to fractions. The difference is instead of showing a numerator over a denominator, a decimal shows portions of a number using a decimal point. Whether the number falls on the left or right of the decimal, each number has a specific place value.
For example, take the following number.
123.456
Hundreds  Tens  Ones  Decimal  Tenths  Hundredths  Thousandths 
1  2  3  .  4  5  6 
Starting from the decimal moving left: the number 3 is in the ones place, the number 2 is in the tens place, and the number 1 is in the hundreds place.
Starting from the decimal moving right: the number 4 is in the tenths place, the number 5 is in the hundredths place, and the number 6 is in the thousandths place. It’s important to note that every number to the right of the decimal ends in th.
COMPARING DECIMALS
Comparing decimals may seem scary. Once you understand how the decimal is broken down then you can answer comparison questions easily.
For example: Which of the following decimals are larger: 0.5 or 0.6?
Ones  Decimal  Tenths 
0  .  5 
0  .  6 
Both the decimals above have the same ones’ place value. The tenths place value is the first instance where the numbers are different. Which number is larger: 5 or 6? 6 is larger than 5, the decimal 0.6 is larger.
Continue to compare numbers when decimals contain more than one place value.
For example: Which of the following decimals are smaller: 0.56 or 0.58?
Ones  Decimal  Tenths  Hundredths 
0  .  5  6 
0  .  5  8 
Both the decimals above have the same ones’ place value so we will continue to compare the numbers after the decimal. The tenths place value has the same value and the hundredths place value is the first instance where the numbers are different. Which number is smaller: 6 or 8? 6 is less than 8, the decimal 0.56 is smaller.
UNDERSTANDING ADDITION WITH DECIMALS
Adding decimals are performed just as you would with whole numbers. The trick is to keep the decimal points lined up while performing your operation.
For example, simplify the operation: 2.345 + 1.67.
We start by lining up the decimals and adding a zero in the thousandths place value:
2 . 3 4 5
+ 1 . 6 7 0
4 . 0 1 5
The correct answer is 4.015.
UNDERSTANDING SUBTRACTION WITH DECIMALS
When subtracting decimals, continue to keep the decimal points lined up as you perform the operation and subtract as you would whole numbers.
For example, simplify the operation: 24.56 – 4.102.
We start by lining up the decimals and adding a zero in the thousandths place value:
2 4 . 5 6 0
– 4 . 1 0 2
2 0 . 4 5 8
The correct answer is 20.458.
UNDERSTANDING MULTIPLICATION WITH DECIMALS
Multiplication can be slightly trickier than addition and subtraction. Perform multiplication of decimals as you would with whole numbers. Then count the number of place values to the right of the decimal and insert the decimal point in the result.
For example, simplify the operation: 0.04 x 0.6.
For this equation, begin by multiplying 4 times 6. The product is 24. Then, count the number of place values to the right of the decimal. The decimal 0.04 has two place values to the right of the decimal and 0.6 has one place value to the right of the decimal. The final answer must have three place values after the decimal. Starting with your answer 24, count to the left 3 decimal places to the left. Add zeros as you love to the left.
The correct answer is 0.024.
UNDERSTANDING DIVISION WITH DECIMALS
Division is performed much like multiplication. Performing division is slightly different depending on whether the operation is using whole numbers or decimal numbers.
If you are dividing by whole numbers, place the decimal directly above the number being divided in the same location.
Simplify the operation: 4.2625 ÷ 5
0.8525
5
– 40
26
– 25
12
– 10
25
– 25
0
The correct answer is 0.8525.
If you are dividing two decimal numbers, you can change the decimal location by moving the decimal to the right equally in both decimals. For example: 8.4 ÷ 0.7 becomes 84 ÷ 7. In both decimals, we moved the decimal location to the right one time creating whole numbers.
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