A decimal number uses a decimal point to show parts of a whole that are less than one. The digits to the right of the decimal point represent tenths, hundredths, thousandths, and so on.
- Place Value in Decimals
- Consider 47.326:
- 4 is in the tens place (value = 40)
- 7 is in the ones place (value = 7)
- 3 is in the tenths place (value = 3/10 = 0.3)
- 2 is in the hundredths place (value = 2/100 = 0.02)
- 6 is in the thousandths place (value = 6/1000 = 0.006)
Reading Decimals
47.326 is read as "forty-seven point three two six" or "forty-seven and three hundred twenty-six thousandths."
Equivalent Decimals
Adding zeros to the right of a decimal does not change its value:
0.5 = 0.50 = 0.500.
- Comparing Decimals
- Compare whole number parts first.
- If equal, compare tenths digits, then hundredths, etc.
Converting Fractions to Decimals
Divide numerator by denominator:
3/4 = 3 ÷ 4 = 0.75.
Or write as fraction with denominator 10/100/1000:
7/10 = 0.7; 25/100 = 0.25.
Addition and Subtraction of Decimals
Align the decimal points, then add or subtract.
Write 0.7 in fraction form.
0.7 = 7/10.
Compare 0.35 and 0.352.
0.350 vs 0.352. Same up to hundredths. At thousandths: 0 < 2. So 0.35 < 0.352.
Add 14.76 + 8.9 + 0.045.
Align: 14.760 + 8.900 + 0.045 = 23.705.
Subtract 12.5 - 6.38.
12.50 - 6.38 = 6.12.
Convert 3/8 to decimal.
3 ÷ 8 = 0.375.
A rope is 5.65 m long. After cutting off 2.8 m, what length remains?
5.65 - 2.80 = 2.85 m.
Seema has Rs 125.50 and spends Rs 78.75. How much is left?
125.50 - 78.75 = Rs 46.75.
- Key Facts
- The decimal point separates the whole number part from the fractional part.
- To add/subtract: align decimal points, add zeros as placeholders if needed.
- Moving the decimal one place to the right multiplies by 10; one place left divides by 10.
Common mistakes
- Forgetting to align decimal points during addition/subtraction.
- Treating 0.3 and 0.30 differently — they are equal.
- Comparing 1.09 and 1.9 as equal (they are not: 1.9 > 1.09).
Summary
Decimals extend the place value system to represent fractions. Each decimal place is a power of 10 below 1. Addition and subtraction require aligning decimal points. Decimals are used in everyday measurements of length, weight, and money.