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The HCF of the numbers 0.24, 1.2, and 0.06 is:
0.06
0.6
0.012
0.12
0.06
Convert all decimals to the same number of decimal places (0.24, 1.20, 0.06). Ignore the decimal point, find the HCF of the integers (24, 120, 6), which is 6, then place the decimal back at the same position (two places).
Three decimal numbers are provided: 0.24, 1.2, and 0.06.
HCF┬аof┬аDecimals=LCM┬аof┬аDenominatorsHCF┬аof┬аNumeratorsтАЛ
Convert all decimals to the same number of decimal places (0.24, 1.20, 0.06). Ignore the decimal point, find the HCF of the integers (24, 120, 6), which is 6, then place the decimal back at the same position (two places).
Students often fail to equalize the number of decimal places before finding the HCF, leading to incorrect calculations like taking the HCF of 24, 12, and 6 instead of 24, 120, and 6.
Convert to common decimal places
To make calculation consistent, express all numbers with two decimal places: 0.24, 1.20, and 0.06.
0.24,1.20,0.06
Convert to fractions
Convert these decimals into fractions with a denominator of 100: 10024тАЛ, 100120тАЛ, and 1006тАЛ.
10024тАЛ,100120тАЛ,1006тАЛ
Apply HCF of fractions formula
The formula for HCF of fractions is the HCF of numerators (24, 120, 6) divided by the LCM of denominators (100, 100, 100).
HCF=LCM(100,100,100)HCF(24,120,6)тАЛ
Calculate the result
The HCF of 24, 120, and 6 is 6. The LCM of 100, 100, and 100 is 100. Thus, the HCF is 1006тАЛ=0.06.
1006тАЛ=0.06
A is correct because the greatest common divisor of 24, 120, and 6 is 6, which when adjusted for the decimal point results in 0.06.
This method is essentially the same as finding the HCF of numbers in a ratio; always scale integers to the same power of 10 to avoid fractional errors.