DECIMALS

DECIMALS

Chapter 3

There are many aspects in everyday life where you can see the use of decimals.

For example, measurements such as length, weight, time, capacity, area, volume, and distance are often expressed in decimals.

Scores in certain sports such as gymnastics are also given in decimals.

Your knowledge on money, on the other hand, builds on your understanding of decimals.

Decimals Through Ten Thousandths

Lesson 1

The first one is a whole figure. If you divide this figure into 10 equal parts, you will get the second figure. The shaded part is equivalent to 1/10.

Each of the 10 equal parts in the second figure is further divided into 10 equal parts. You can see from the last figure that there are now 100 equal parts. The shaded part is equivalent to 1/100.

You have learned in the previous grade that 1/10 is equivalent to 0.1. 

Looking at the third figure above, you can say that 1/100 is equivalent to 0.01.

If you further divide each of the 100 equal parts in the third figure into 10 more equal parts, each part is equivalent to 1/1000 or 0.001. 

Thus, if you still further divide each of the 1000 equal parts into 10 equal parts, each part is equivalent to 1/10000 or 0.0001.

Numbers such as 0.1, 0.01, 0.001, and 0.0001 are called decimals.

decimal

is a number that can be expressed as a fraction whose denominator is a power of 10. 

A  mixed decimal consists of a whole number and a decimal.

Each digit has its corresponding value. Note that the  decimal point  is used to separate the whole numbers from the decimals.

In the decimal 43.2857, the digit 2 is in the  tenths  place, which is one place to the right of the decimal point. The value of the digit 2 is 2 tenths.

The digit 8 is in the hundredths place, which is two places to the right of the decimal point. The value of the digit 8 is 8 hundredths.

The digit 5 is in the  thousandths  place, which is three places to the right of the decimal point. The value of the digit 5 is 5 thousandths.

The digit 7 is in the  ten thousandths  place, which is four places to the right of the decimal point. The value of the digit 7 is 7 ten thousandths.

Let Us Practice

• Write the value of the underlined digit in each decimal.

• Are you ready?

• Let's start!

Work Together

• For each decimal, identify the digit in the tenths place.

• Are you ready?

• Let's start!

Work Together

• For each decimal, identify the digit in the hundredths place.

• Are you ready?

• Let's start!

Work Together

• For each decimal, identify the digit in the thousandths place and the digit in the ten thousandths place.

• example: 9[space]2 (you need to have space between the number). It will look like this, 9 2.

• Are you ready?

• Let's start!

Work Alone

• Write on the line the place value of the underlined digit.

• Are you ready?

• Let's start!

Work Alone

• Write on the line the value of the underlined digit.

• Are you ready?

• Let's start!

Let Us Solve

• Identify the letter of the decimal number that matches each description.

• Are you ready?

• Let's start!

Multiple Choice

I have a 3 in my hundredths place. I have a number greater than 0 in my tenths place.

• a. 0.226

• b. 0.4046

• c. 6.06

• d. 2.136

• e. 5.325

Multiple Choice

I have a 0 in my hundredths place. I am less than 1.

• a. 0.226

• b. 0.4046

• c. 6.06

• d. 2.136

• e. 5.325

Multiple Choice

I have a 6 in my thousandths place. Two of my digits are the same.

• a. 0.226

• b. 0.4046

• c. 6.06

• d. 2.136

• e. 5.325

Multiple Choice

I have 0 in my tenths place. Two of my digits are the same.

• a. 0.226

• b. 0.4046

• c. 6.06

• d. 2.136

• e. 5.325

Reading and Writing Decimals

Lesson 2

Recall that every digit to the right of the decimal point has a decimal place. For example, the decimal 42.37 has two decimal places. On the other hand, 42.3 has only one decimal place.

The number 42.375 has three decimal places.

Going back to the number in the place value chart, the following are the value of each digit in its decimal places.

•  3: 3 tenths or 3/10

• You write 3 tenths as 0.3.

Going back to the number in the place value chart, the following are the value of each digit in its decimal places.

• 7: 7 hundredths or 7/100

• You write 7 hundredths as 0.07.

Going back to the number in the place value chart, the following are the value of each digit in its decimal places.

• 5: 5 thousandths or 5/1000

• You write 5 thousandths as 0.005.

You read the decimal 42.375 as

“forty-two and three hundred seventy-five thousandths.” 

You read decimals just like whole numbers. However, you state the place value of the last decimal digit.

Note that the decimal point is read as “and.” The numbers that come before a decimal point are whole numbers.

The decimal 42.375 can also be written in different ways.

Thus, the decimal 42.375 is equivalent to any one of the following.

Study these examples.

• The decimal 8.5 is read as “eight and five tenths.”

• The decimal 15.64 is read as “fifteen and sixty-four hundredths.”

• The decimal 42.186 is read as “forty-two and one hundred eighty-six thousandths.”

• The decimal 8.2645 is read as “eight and two thousand six hundred forty-five ten thousandths.”

Study these examples.

• Three and four tenths is written as 3.4.

• Two and fifteen hundredths is written as 2.15.

• Sixteen and three hundred eighty-one thousandths is written as 16.381.

• Twelve and five hundred thirty-six ten thousandths is written as 12.0536.

Get Ready

• On the line, write each decimal given the value of the digits.

• Are you ready?

• Let's start!

• 
  

Work Together

• Write on the line each decimal in standard form.

• Are you ready?

• Let's start!

Assignment:

Answer "Work Alone" and "Lest Us Solve"

page 131