Grade 7 → Number System ↓
Decimals
Decimals are an important part of the number system that helps us express fractions and more precise values. In mathematics, decimals are used to represent numbers that are not whole. Understanding decimals is essential because they are commonly used in everyday life, such as in money calculations, measurements, and statistical data.
What are decimals?
Decimals are numbers that are expressed as a whole number part and a fraction part separated by a decimal point. For example, the number 5.32
consists of the whole number 5
, the decimal point, and the fraction 32/100
.
Here is a simple division of a decimal number:
Whole Number Decimal Digit Fractional Part 5. 32
Place value in decimal
Just like whole numbers, decimals also have place values. The position of each digit in a decimal number determines its value. Let us look at place values in decimal numbers:
thousands hundreds tens units tenths hundredths thousandths 0 0 0 5 . 3 2
In number 5.32
:
5
is in the 'units' place.3
is in the '10th' place.2
is in the 'hundredths' place.
Reading and writing decimals
When you read decimals, say the whole number part first, then say the decimal point as "point," followed by saying each digit of the fractional part separately. For example:
3.14
would read "three point one four."7.05
would be read as "seven point zero five".
To write a decimal, write the whole number part, followed by a period (.) for the decimal point, and then write the digits of the fractional part. For example, "twenty-three decimal four five six" is written as 23.456
.
Decimal fraction
Decimals are essentially another way to write fractions. Every decimal has an equivalent fraction representation.
Example:
0.5
=5/10 = 1/2
0.75
=75/100 = 3/4
0.25
=25/100 = 1/4
Converting decimals to fractions
To convert a decimal to a fraction, follow these steps:
- Write the decimal after dividing by 1.
- Multiply both the numerator and denominator by 10 for each digit after the decimal point.
- Simplify the fraction, if possible.
Example: Convert 0.75
to a fraction.
Step 1: 0.75 = 0.75/1 Step 2: Multiply by 100 = 75/100 Step 3: Simplify = 3/4
Converting fractions to decimals
To convert a fraction to a decimal, divide the numerator by the denominator.
Example: Convert 3/4
to a decimal.
3 ÷ 4 = 0.75
Adding and subtracting decimals
Adding and subtracting decimals is similar to adding and subtracting whole numbers. Here's how to do it:
- Align the decimal points.
- Start adding or subtracting from the rightmost digit (like whole numbers).
- Place the decimal point in the sum in the same place as the numbers above.
Example: Add 3.25
and 4.6
.
3.25 + 4.60 , 7.85
Multiplying decimals
To multiply decimals:
- Ignore the decimal points and multiply the numbers as if they were whole numbers.
- Count the total number of decimal places in both numbers.
- Place the decimal point in your answer so that it has the same number of decimal places.
Example: Multiply 1.2
by 3.4
.
1.2 × 3.4 , 48 (1.2×4) + 360 (1.2×3; move one place left) , = 4.08
Dividing decimals
To divide one decimal by another:
- Move the decimal point in the divisor to make it a whole number.
- Move the decimal point in the dividend the same number of places.
- Divide as usual, placing the decimal point in the quotient directly above its place in the dividend.
Example: 6.6
divided by 1.1
.
6.6 ÷ 1.1 = 66 ÷ 11 = 6
Decimal rounding
Rounding decimals is useful when you need approximate numbers. Here's how to round to a specific place value:
- Find the place value you want to round off.
- Look at the number immediately to the right.
- If that digit is 5 or greater, increase the selected place value digit by 1.
- If that score is less than 5, leave the selected score unchanged.
- Delete all digits to the right of the selected position.
Example: Round off 5.678
to the nearest tenth.
The digit in tenth place is 6. The next digit is 7 (which is greater than 5). So round it off to 5.7.
Practice problems
- Convert the fraction
7/8
to a decimal. - Add
4.56
and7.89
. - Multiply
0.6
by0.75
. - Divide
9.0
by3.0
. - Round off
2.467
to the nearest hundred.
By practicing these problems, one can become more comfortable with decimals in various mathematical operations.