# ATI TEAS GUIDE TO MATH | BASIC DECIMALS

## UNDERSTANDING DECIMALS

DECIMALS – Full Page Slides

DECIMALS – Multiple Slides

DECIMALS – Slides with Notes

### QUIZ QUESTIONS LISTED AT END OF REVIEW

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.

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

## 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

## 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.

## 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