Chapter 3
274 Words
Decimals
3.1 Introduction to Decimals
A decimal is another way to represent fractions. It uses powers of 10 to express parts of a whole. The decimal point separates the whole number part from the fractional part.
Example: The decimal 0.75 represents the fraction 75100frac{75}{100}10075.
3.2 Converting Fractions to Decimals
To convert a fraction to a decimal, divide the numerator by the denominator.
Example: 34=0.75frac{3}{4} = 0.7543=0.75
3.3 Converting Decimals to Fractions
To convert a decimal to a fraction, count the number of decimal places, and write the decimal as a fraction over a power of 10.
Example: 0.6 can be written as 610frac{6}{10}106, which simplifies to 35frac{3}{5}53.
3.4 Operations with Decimals
Addition and Subtraction: When adding or subtracting decimals, align the decimal points before performing the operation.
Example:
5.75+3.4=9.155.75 + 3.4 = 9.155.75+3.4=9.15
Multiplication: To multiply decimals, multiply the numbers as if they were whole numbers, then count the total number of decimal places in the numbers and place the decimal point accordingly.
Example:
0.3×0.4=0.120.3 times 0.4 = 0.120.3×0.4=0.12
Division: To divide decimals, move the decimal point to the right in both the divisor and the dividend until the divisor is a whole number, then divide as usual.
Example:
2.4÷0.6=42.4 div 0.6 = 42.4÷0.6=4Exercises
Exercise 1: Convert the following fractions to decimals:
12frac{1}{2}21
35frac{3}{5}53
78frac{7}{8}87
910frac{9}{10}109
425frac{4}{25}254
Exercise 2: Convert the following decimals to fractions:
0.5
0.75
1.25
0.4
0.8
Exercise 3: Perform the following operations with decimals:
12.5 + 7.8
6.9 - 4.3
3.6 × 0.5
9.6 ÷ 3
0.24 × 0.5
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