### Key Concepts

- Expressing fractions in tenths as decimals.
- Expressing fractions in hundredths as decimals.
- Comparing and ordering decimals.
- Number patterns.

**Introduction:**

- In this chapter, we will learn to express fractions as equivalent fractions with a denominator 10.
- Simplifying fractions with a denominator of 10.
- Rounding numbers to the nearest ten.
- Knowing fractions and mixed numbers.

**Fractions: **

Fractions are represented as numerical values and can be defined as the parts of a whole.

**Parts of Fraction: **

All fractions consist of a **numerator** and a **denominator**.

- The
**denominator**indicates how many parts the whole has been divided into. It is placed in the lower part of the fraction. - The
**numerator**indicates how many sections of the fraction are represented. It is placed in the upper part of the whole.

**Example:**

**Example:**

**Understanding Tenths:**

**Decimals:** A decimal number can be defined as a number whose whole number part and the decimal point separates the fractional part. The dot in a decimal number is called a decimal point.

**Read and write tenths in decimal and fractional forms.**

**Tenths:** The first digit to the right of the decimal point is one out of 10 equal parts of a whole.

**Example:**

**Example:** 0.6 means six-tenths or

**Decimal form:** A decimal is a fraction written in a particular form.

**Example:**

**E.g.,** Instead of writing

You can express the fraction as 0.5.

**Decimal point:** A point used to separate the whole number part from the fractional part of the decimal number.

**Example:**

**Example:** 34.9

Here, 34 = Whole number part

9 = Fractional part

. = Decimal

**Expanded form:** The expanded notation, also called expanded form, for decimals is the same as the integer expanded form. A decimal can be written as the sum of all the place values.

**E.g.,** (a) Write 317.29 in an expanded form.

**Sol:**

**Place value chart:**

**Example:** Write the place value of the digits 2 and 4 in the number 326.471

**Sol:**

Place value of 2 = Tens = 20

Place value of 4 = Tenths = 0.4

**Understanding Hundredths:**

**Hundredths:** Divide one whole into 100 equal parts or one-hundredth. In the decimal form, each part has a value equal to 0.01.

**Example:** Express the fraction in decimal?

**Place holder zero:** The zero is called a place holder. It is not worth anything on its own, but it changes the value of other digits.

Look at the number 502.

**Sol: 52 = five tens and two units**

The zero place-holder is keeping the 5 and 2 in their correct places:

**Examples: **

(a) Express as a decimal.

** Sol:** = 0.05

(b) Express 15 hundredths as decimal.

**Sol:** = 0.15

(c) Express 1 as decimal

**Sol:**

1 = 1 one and 2 tenths 5 hundredths

= 1 one and 25 hundredths

= 1.25

**Comparing Decimals:**

**Compare and order decimals.**

**Comparing Decimals:** Comparing means examining the differences between numbers, quantities, or values to decide if it is greater than, smaller than, or equal to other quantities.

**Example:** Compare 4.27 and 4.65 using a number line.

**Sol:**

**Example: **

(a) Compare 0.6 and 0.8

** Sol:** 0.6 = 6 tenths

0.8 = 8 tenths

Because 8 tenths > 6 tenths

0.8 > 0.6

(b) Compare 0.317 and 0.341

**Sol:** 0.317 = 0.3 + 0.01 + 0.007

= 3 tenths + 1 hundredths + 7 thousandths

0.341 = 0.3 + 0.04 + 0.001

= 3 tenths + 4 hundredths + 1 thousandths

3 tenths = 3 tenths

Now, compare the next digit

1 hundredths < 4 hundredths

Thus, 0.317 < 0.341

**Ordering:** Arranging things in relation to each other according to a particular sequence or a pattern.

**Example:**

(a) Order 9.34, 83.9, 21.4, 0.96 from smallest to largest.

**Sol:** 0.96, 9.34, 21.4, 83.9

(b) Order 7.93, 5.94, 0.93, 28.7 from largest to smallest.

**Sol:** 28.7, 7.93, 5.94, 0.93

**Complete number patterns**

Number pattern is a pattern or sequence in a series of numbers by using a specific rule or pattern.

**Example:** (a) Complete the pattern 1.5, 1.9, 2.3, 2.7, 3.1, 3.5, 3.9, ____, ____

**Sol:**

(b) Find the next two numbers in the pattern 6.8, 6.4, 6, 5.6, 5.2, 4.8, 4.4.

**Sol:**

### What have we learnt:

- Introduction of decimals.
- How the place value of a digit changes when we multiply or divide by ten.
- How to read, write, and model fractions with 10 and 100 in the denominator.
- How to compare decimals from the least to greatest and from the greatest to least.
- Ordering of decimals.

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