Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will see how a decimal, a simple dot, can change the place value of all the digits in a number. You will also learn how to read decimals using place values.

Before we can talk about decimal place values, we need to quickly review what a decimal is. **Decimals** are numbers with one visible point or dot somewhere in the number. This point is called the **decimal point**.

We actually see them everywhere around us, especially when we go shopping. What do we see on most everything we purchase? Well, we see a price tag. What kinds of numbers do you most often see on price tags? That's right! You see decimals! You see things like 6.99, 1.99, 0.99 and so on.

All those numbers you see on price tags and every other number you see and encounter must follow the rules of place values. What exactly is a place value? Well, a **place value** tells you the location of each digit in a number. The number 699, for example, has a 9 in the units place, a 9 in the tens place and a 6 in the hundreds place. All numbers follow the same place value naming criteria.

The number 211 has a 1 in the units place, a 1 in the tens place and a 2 in the hundreds place. The number 423 has a 3 in the units place, a 2 in the tens place and a 4 in the hundreds place. Notice how the tens place is always the second digit to the left and that the hundreds place is always the third digit to the left. Believe it or not, you already know most of the place values since you use them to count. Look at this large number broken down into its place values. The number is 123,456.

Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Units |
---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 |

How would you say this number? Yes, you would say one hundred twenty-three thousand four hundred and fifty-six. Let's break this down into its place values. While we read from the left to the right, we will read our place values from the right to the left, in the opposite direction. We have 6 units, 5 tens, 4 hundreds, 3 thousands, 2 ten thousands and 1 hundred thousand. If you were asked how many hundreds there are in 123,456, you would answer 4 because there are 4 hundreds in that number.

You can think of the number as an addition problem. 123,456 is the same as 100,000, plus 20,000, plus 3,000, plus 400, plus 50, plus 6. Just like our place values told us, we have 1 hundred thousand, 2 ten thousands, 3 thousands, 4 hundreds, 5 tens and 6 units.

When you add a decimal point into the mix, the location of the decimal point now determines your place values. Your decimal point tells you where to begin counting. The decimal number 6.99 has a 6 in the units place. The units place value is always the first number to the left of the decimal. To count your place values to the right of the decimal, you start from the left and go to the right.

So essentially, to count place values, you always start from the decimal and work your way out. Remember that every number has a decimal, even if none is shown. The numbers 211 and 423 both have a decimal point at the end, but we don't write it or show it because there are no numbers after it.

When you have a decimal, the place values will look like this:

Units | . | Tenths | Hundredths | Thousandths | Ten Thousandths | Hundred Thousandths |
---|---|---|---|---|---|---|

1 | . | 2 | 3 | 4 | 5 | 6 |

Notice here that you begin with tenths when you go the right of the decimal point and that you begin with the units when you go to the left. We know what tens, hundreds and thousands mean, but what about tenths, hundredths and thousandths? What do they mean? A tenth means one tenth or 1/10. In decimal form, it is 0.1. Notice the position of the 1. It's in the tenths place. 'Hundredth' means a hundredth or 1/100. In decimal form, it is 0.01.

Notice again the position of the 1. Where is it at? That's right, in the hundredths place. As we continue to the right, the numbers will continue to get smaller, with each step being 10 times smaller than the one before. Going to the left, each place value is bigger than the previous by 10 times. If you wanted to tell someone how many tenths a certain decimal number has, you would find the location of that place value and tell him or her the number that's there. For the number 1.23456, there are 2 tenths.

Like regular numbers, you can also think of decimal numbers as addition problems. The only difference would be that your last addition is a fraction of everything after the decimal. You can think of 0.7 as 0 plus 7/10. We are dividing by 10 because that's what the tenth place tells us to do.

If we have 1.23, we can rewrite it as 1 plus 23/100 since the hundredths place tells us to divide by 100. What about a number like 1.234? How would you write that? Yes, you can write that as 1 plus 234/1000 since the last place value is the thousandths place, which is telling us to divide by a thousand.

When you read decimals out loud, you will use the place values. The number 0.7 would read as seven tenths. The number 1.23 would read as one point twenty three hundredths. Like regular numbers, you also read decimal numbers from the left to the right. So, when you have a decimal number, your end word will be the last place value that you reach.

To review, **decimals** are numbers with a point somewhere in the number. That point is called a **decimal point**. The **place values** are counted from the decimal point. Going to the left, they are units, tens, hundreds, thousands, ten thousands, hundred thousands and so on. Going to the right, they are tenths, hundredths, thousandths, ten thousandths, hundred thousandths and so on.

Each place value is 10 times bigger than the place value to its right or 10 times smaller than the place value to its left. When you are looking at any number, going to the right means your numbers are getting smaller, and going to the left means your numbers are getting bigger. When you read numbers, you are actually basing it off their place values.

Upon completing this lesson, you will be able to:

- Define decimals and decimal points
- Identify place values to either side of a decimal point
- Read decimals out loud

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
1 in chapter 3 of the course:

Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

- What is a Decimal Place Value? 6:19
- Arithmetic with Decimal Numbers 10:40
- Solving Problems Using Decimal Numbers 6:57
- What is a Percent? - Definition & Examples 4:20
- Changing Between Decimals and Percents 4:53
- Solve Problems Using Percents 7:50
- Changing Between Decimals and Fractions 7:17
- Go to ELM Test - Numbers and Data: Decimals and Percents

- CSET Spanish Subtest III (147): Study Guide & Practice
- Praxis Elementary Education - Instructional Practice & Applications (5019): Study Guide & Practice
- OSAT Mild-Moderate Disabilities (CEOE) (129): Study Guide & Practice
- OSAT English as a Second Language (CEOE) (077): Study Guide & Practice
- CSET Spanish Subtest I (145): Study Guide & Practice
- Energy Transformations & Thermodynamics
- Using Different Types of Student Assessments
- Homeostasis & Health Maintenance
- Alignment of Texas Science Instruction for High Schoolers
- Teaching Strategies for High School Science
- How Long is the HESI A2 Nursing Exam?
- What is the HESI A2 Admission Assessment Exam?
- AFOQT Accommodations
- AFOQT Test Day Preparation
- Difference Between HESI & HESI A2 Nursing Exams
- Passing the HESI A2 Nursing Exam
- HESI Test Retake Policy

- Collaborative Approaches in Special Education: Strengths & Limitations
- Teaching Literacy to Students with Severe Disabilities
- What is a Ligand in Cell Biology?
- The Secret Garden Book Summary
- Using Excel for Descriptive Statistics
- Software Engineering - Assignment 1: Configuration Management
- Geometric Distribution: Definition, Equations & Examples
- Generating Function in Discrete Math: Definition & Examples
- Quiz & Worksheet - Adding Whole Numbers & Fractions
- Quiz & Worksheet - Teaching Students with Literacy Disabilities
- Quiz & Worksheet - Internal Hemorrhaging in Legs
- Quiz & Worksheet - Deaf or Hard of Hearing Students
- Quiz & Worksheet - How to Teach Critical Thinking Skills
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- American Revolution Study Guide
- Business Law in Sales
- English 305: Advanced Technical Writing
- High School Biology: Help and Review
- NY Regents Exam - Living Environment: Tutoring Solution
- Human Reproductive Systems: Homeschool Curriculum
- TExMaT Master Mathematics Teacher 8-12: Radical Expressions
- Quiz & Worksheet - One Point Perspective Drawing
- Quiz & Worksheet - Understanding Moral Nihilism
- Quiz & Worksheet - How Islam Spread in West Africa
- Quiz & Worksheet - Jarvis Lorry in A Tale of Two Cities
- Quiz & Worksheet - Topic vs. Argument in a Reading Passage

- Westward U.S. Expansion (1820-1860)
- Comparisons of 18th Century Satire: Alexander Pope vs. Jonathan Swift
- Is the FTCE Middle Grades English 5-9 Test Difficult to Take?
- Background Checks for Teachers
- How to Study for Chemistry in College
- Sequencing Activities for Kindergarten
- Adjectives Lesson Plan
- Phases of the Moon Lesson Plan
- How to Study for a Science Test
- Distributive Property Lesson Plan
- Adult Literacy Resources
- Finding Illinois TAP Testing Centers

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject