can we find. the HCF of 1.2 and 1.02 ? justify your answer
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We cannot directly find a solution to the GCD of two decimals. But there is a way :
Make it a whole number.
See the steps below :
1. Make them a whole number by multiplying it with a power of 10. (both should be multiplied with the same number)
1.2 × 10² = 120
1.02 × 10² = 102
2. Find the GCD of the two results.
120 = 2 × 2 × 2 × 3 ×5
102 = 2 × 3 × 17
Common Factors ⇒ 2¹ × 3¹
∴gcd ( 120,102 ) = 2 × 3 = 6
3. Multiply the GCD by the inverse of the power of ten the decimals were multiplied with.
6 × r ( 10² ) = 0.6
Ans=0.6
Make it a whole number.
See the steps below :
1. Make them a whole number by multiplying it with a power of 10. (both should be multiplied with the same number)
1.2 × 10² = 120
1.02 × 10² = 102
2. Find the GCD of the two results.
120 = 2 × 2 × 2 × 3 ×5
102 = 2 × 3 × 17
Common Factors ⇒ 2¹ × 3¹
∴gcd ( 120,102 ) = 2 × 3 = 6
3. Multiply the GCD by the inverse of the power of ten the decimals were multiplied with.
6 × r ( 10² ) = 0.6
Ans=0.6
Answered by
13
Answer:
Step-by-step explanation:
Let’s take two fractions (a/b) and (c/d).
To find LCM and HCF of (a/b) and (c/d) the generalized formula will be:
H.C.F = H.C.F of numerators / L.C.M of denominators
L.C.M = L.C.M of numerators / H.C.F of denominators
so,HCF of (1.2 , 0.12) =HCF of (12/10 , 12/100)=HCF of (12, 12) /LCM of (10, 100)
since=>HCF of (12 , 12) = 12 and LCM of (10 , 100) = 100
so, HCF of (1.2 , 0.12) =12/100 =0.12
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