without actual division show that each of the following rational numbers is a terminating decimal Express each in decimal form:
1. 33/50
2. 11/625
3. 24/125
4. 171/800.
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1.33/50=3/(25×2)=3/(5^2 × 2^1)
As the denominator of the given fraction can be expressed in the form 2^m ×5^n,so it is a terminating decimal.
now,
33/(5^2 × 2)= (33×2)/(5^2×2^2)=66/100=0.66
2.625 can be expressed as 5^4 × 2^0 which is in the form 2^m × 5^n. So it's also a terminating decimal.
11/625=(11×2^4)/(625×2^4)=(11×16)/(625×16)=176/10000=0.0176
Q.no.- 3 & 4 are both terminating & have terminating decimal expressions.So find it out for yourself.
As the denominator of the given fraction can be expressed in the form 2^m ×5^n,so it is a terminating decimal.
now,
33/(5^2 × 2)= (33×2)/(5^2×2^2)=66/100=0.66
2.625 can be expressed as 5^4 × 2^0 which is in the form 2^m × 5^n. So it's also a terminating decimal.
11/625=(11×2^4)/(625×2^4)=(11×16)/(625×16)=176/10000=0.0176
Q.no.- 3 & 4 are both terminating & have terminating decimal expressions.So find it out for yourself.
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