Write down the decimal expansion of 76/6250 without actual division
Answers
Answer:
The decimal expansion of 76/6250 is 0.01216.
Step-by-step explanation:
To find the decimal expansion of a number without actual dividing, multiply both the numerators and denominators with a constant k. First,, find the value of k, and then multiply such that the denominator becomes in the form of 10^n where n is an integer.
Given 76/6250
expressing the given expression in the form of prime multiples
76/6250 = 2×2×19/5×5×5×5×5×2
multiplying and dividing by 2×2×2×2 so that denominator becomes 10^5
=2×2×19×2×2×2×2 / 5×5×5×5×5×2×2×2×2×2
=1216/10×10×10×10×10
=1216/100000
=0.01216
The decimal expansion of 76/6250 is 0.01216
0R
Given, 76/6,250
=76/6,250×16/16
=16(50+25+1)/100,000
=800/100,000+400/100,000+16/100,000
=0.008+0.004+0.00016
=0.01216