Decimals - Revision Notes

 CBSE Class 6 Mathematics

Revision Notes
CHAPTER – 8
Decimals


  • To understand the parts of one whole (i.e. a unit) we represent a unit by a block. One block divided into 10 equal parts means each part is 110 (one-tenth) of a unit. It can be written as 0.1 in decimal notation. The dot represents the decimal point and it comes between the units place and the tenths place.
  • Every fraction with denominator 10 can be written in decimal notation and vice-versa.
  • One block divided into 100 equal parts means each part is 110 (one-hundredth) of a unit. It can be written as 0.01 in decimal notation.
  • Every fraction with denominator 100 can be written in decimal notation and vice-versa.
  • In the place value table, as we go from left to the right, the multiplying factor becomesof the previous factor.
  • Fractions as Decimals: Fractions can be converted into decimals by writing them in the form with denominators 10, 100 and so on. Example: 710=0.7
  • Decimals as Fractions: Decimals can be converted into fractions by removing their decimal points and writing 10, 100, etc. in the denominators, depending upon the number of decimal places in the decimals. Examples: 0.9 = 910
  • Addition of Decimals: Decimals can be added by writing them with equal number of decimals places. Example: add 0.005, 6.5 snd 20.04.
    Solution: Convert the given decimals as 0.005, 6.500 and 20.040.
    0.005 + 6.500 + 20.040 = 26.545
  • Subtraction of Decimals: Decimals can be subtracted by writing them with equal number of decimal places.
    Example: Subtract the given decimals as 5.674 and 12.500
    12.500 – 5.674 = 6.826
  • Comparing Decimals: Decimals numbers can be compared using the idea of place value: Example: 45.32 or 35.69
    The given decimals have distinct whole number part, so we compare whole number part only. The whole number part of 45.32 is greater than 35.69. Therefore, 45.32>35.69.
  • Using Decimals: Many daily life problems can be solved by converting different units of measurements such as money, length, weight, etc. in the decimal form.
  • Money:
    100 paise = 1 Rupee
    1 paise = 1/100 Rupee = 0.01 Rs.
    5 paise = 5/100 Rs. = 0.05 Rs.
    105 paise = 1 Rs. + 5 paise = 1.05 Rs.
    7 Rs. 8 paise = 7 Rs. + 0.08 Rs = 7.08 Rs.
    7 Rs. 80 paise = 7 Rs. + 0.80 Rs. = 7.80 Rs.
  • Length:
    10 mm = 1 cm
    1mm = 1/10 cm = 0.1 cm
    100 cm = 1 m
    1 cm = 1/100 m = 0.01 m
    1000 m = 1 km
    1 m = 1/1000 km = 0.001 km
  • Weight:
    1000 g = 1 kg
    1 g = 1/1000 kg = 0.001 kg
    25 g = 25/1000 kg = 0.025 kg