1. This work is licensed under a Creative Commons Attribution 4
This work is licensed under a Creative Commons Attribution 4.0 International License.

2. Decimals
Module Overview

3. Acknowledgments
This presentation is based on and includes content derived from the following OER resource:
Pre-Algebra
An OpenStax book used for this course may be downloaded for free at:

4. To name a decimal number
Step 1: Name the number to the left of the decimal point
Step 2: Write “and” for the decimal point
Step 3: Name the “number” part to the right of the decimal point as if it were a whole number
Step 4: Name the decimal place of the last digit
Example:
reads as:
“twenty-three and fifty-seven thousandths”
Image: Fig 5.2 Prealgebra, Openstax

5. Write a decimal number from its name
Step 1: Locate the word “and” – it tells you where the decimal point lies. Place a decimal point under the word “and”
Step 2: Translate the words before “and” into the whole number and place it to the left of the decimal point. Note: if there is no “and” write a “0” with a decimal point to its right.
Step 3: Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word
Step 4: Translate the words after “and” into the number to the right of the decimal point. Write the number in the spaces, putting the final digit in the last place. Fill in zeros for place holders, as needed.

6. Example writing a decimal from its name
Two hundred thirty-five and thirty-two thousandths
235.___ ___ ___
Tenths Hundredths Thousands
235.___ _3_ _2_

7. Convert a decimal to a fraction or mixed number

8. Ordering decimals
Step 1: Check to see if both numbers have the same number of decimal places. If not, write zeros at the end of the one with fewer digits to make them match.
Step 2: Compare the numbers to the right of the decimal point as if they were whole numbers.
Step 3: Order the numbers using the appropriate inequality sign.
Example:
vs   > 0.410
0.410

9. Rounding decimals
Step 1: Locate the given place value, and underline the digit to the right.
Step 2: If the underlined digit is greater than or equal to 5, add 1 to the digit in the given place value. If the underlined digit is 4 or less, do not change the digit in the given place value.
Step 3: Rewrite the number, removing all digits to the right of the given place value.
Example:
Round to the nearest hundredth.
Since 8 > 5, add one to the 7 to get 3.48

10. To add or subtract decimals
Step 1: Write the numbers vertically so the decimal points line up
Step 2: Use zeros as place holders, as needed
Step 3: Add or subtract the numbers as if they were whole numbers. Place the decimal in the answer under the decimal points in the given numbers.
Example:
23.1 – 19.43 
3.67

11. To multiply decimals Step 1: Determine the sign of the product.
Step 2: Write the numbers in vertical format, lining up the numbers on the right.
Step 3: Multiply as if they were whole numbers, temporarily ignoring the decimal points.
Step 4: Place the decimal point. The number of decimal places in the product is the sum of the number of decimal places in the factors. Use zeros as placeholders, as needed.

12. Multiplication example

13. To multiply a decimal by a power of 10

14. To divide a decimal by a whole number

15. Dividing Decimal Numbers

16. To convert a fraction to a decimal

17. Converting a fraction to a decimal example 2

18. Properties of circles
Image: Chapter 5, Prealgebra, Openstax

19. Example problems

20. Solve Equations with Decimals

21. Examples using properties of equality

22. Mean

23. Median

24. Mode
The mode of a set of numbers is the number(s) that occur(s) most frequently.
Note: Some data sets have no mode because all values appear the same number of times. Other data sets have more than one mode.
Example:
Find the mode of the following data:
3, 7, 7, 7, 11, 11, 12, 12, 12, 15
Modes: 7 and 12

25. Probability

26. Rate and ratio

27. Unit rate

28. Unit price

29. Squares and radicals
radicand
radical sign

30. Radical example

31. How to study this module
Read the syllabus or schedule of assignments regularly.
Understand key terms; look up and define all unfamiliar words and terms.
Take notes on your readings, assigned media, and lectures.
Discuss topics with classmates.
Frequently review your notes. Make flow charts and outlines from your notes to help you study for assessments.
Complete all course assessments.

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