krit.club logo

Decimals - Introduction to Decimals

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Definition of Decimals: Decimals are a way of expressing parts of a whole using a decimal point. They are essentially fractions where the denominator is a power of 10, such as 10, 100, or 1000. For example, 0.30.3 is the same as 310\frac{3}{10}.

•

The Decimal Point: The dot used in a decimal number is called the decimal point. It acts as a separator: digits to the left of the point represent whole numbers (Ones, Tens, Hundreds), while digits to the right represent values smaller than one (Tenths, Hundredths).

•

Understanding Tenths: When one whole unit is divided into 10 equal parts, each part is called a 'tenth'. Visually, imagine a long rectangular bar divided into 10 equal sections; shading 1 section represents 110\frac{1}{10} or 0.10.1. In the place value chart, the tenths place is the first position to the right of the decimal point.

•

Understanding Hundredths: When one whole unit is divided into 100 equal parts, each part is called a 'hundredth'. Imagine a large square grid made of 10×1010 \times 10 small squares; shading 1 small square represents 1100\frac{1}{100} or 0.010.01. The hundredths place is the second position to the right of the decimal point.

•

Place Value Chart: The decimal place value system extends to the right. The order of positions from left to right is: Hundreds (100100), Tens (1010), Ones (11), Decimal Point (..), Tenths (110\frac{1}{10}), and Hundredths (1100\frac{1}{100}). For example, in 4.564.56, 4 is in the ones place, 5 is in the tenths place, and 6 is in the hundredths place.

•

Reading Decimals: Decimals are read by saying the whole number part, then 'point', and then each digit of the decimal part individually. For example, 12.7512.75 is read as 'twelve point seven five'. Alternatively, it can be read as 'twelve and seventy-five hundredths'.

•

Converting Fractions to Decimals: A fraction with 10 in the denominator has one digit after the decimal point (e.g., 710=0.7\frac{7}{10} = 0.7). A fraction with 100 in the denominator has two digits after the decimal point (e.g., 9100=0.09\frac{9}{100} = 0.09).

📐Formulae

Decimal Number=Whole Number Part+Decimal Part\text{Decimal Number} = \text{Whole Number Part} + \text{Decimal Part}

110=0.1\frac{1}{10} = 0.1

1100=0.01\frac{1}{100} = 0.01

Expanded Form: a.bc=a+b10+c100\text{Expanded Form: } a.bc = a + \frac{b}{10} + \frac{c}{100}

Tenths Place Value=Digit×110\text{Tenths Place Value} = \text{Digit} \times \frac{1}{10}

Hundredths Place Value=Digit×1100\text{Hundredths Place Value} = \text{Digit} \times \frac{1}{100}

💡Examples

Problem 1:

Write the fraction 45100\frac{45}{100} as a decimal and represent it in expanded form.

Solution:

  1. Convert the fraction to a decimal: Since the denominator is 100100, there must be two digits after the decimal point. So, 45100=0.45\frac{45}{100} = 0.45.
  2. Identify the place values: In 0.450.45, the 44 is in the tenths place and 55 is in the hundredths place.
  3. Write in expanded form: 0+410+51000 + \frac{4}{10} + \frac{5}{100}.

Explanation:

To convert a fraction with 100 as the denominator, we place the numerator after the decimal point. The expanded form shows the specific value of each digit based on its position.

Problem 2:

Convert the decimal 7.087.08 into a fraction and write it in words.

Solution:

  1. Identify the parts: The whole number is 77. The decimal part is .08.08, which represents 88 hundredths.
  2. Write as a mixed fraction: 781007 \frac{8}{100}.
  3. Write in words: 'Seven point zero eight' or 'Seven and eight hundredths'.

Explanation:

The digit 0 in the tenths place means there are zero tenths, and the 8 is in the hundredths place. When writing as a fraction, the number of decimal places determines the power of 10 in the denominator.