Arithmetic

102.84÷0.2

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Rewrite division as a fraction

Writing division as a fraction makes it easier to see what we need to simplify. We want to find how many times 0.2 goes into 102.84.
2

Eliminate the decimal by multiplying

Multiply both the top and bottom by 10. This removes the decimal from 0.2 without changing the value of the fraction.
3

Eliminate remaining decimal

There is still a decimal in 1028.4, so we multiply both top and bottom by 10 again. Now we have whole numbers only.
4

Divide whole numbers

Divide 10284 by 20. 20 goes into 10284 exactly 514.2 times. This is our final result.

Understanding this problem

Learning Insight

When you divide by a decimal, you are really asking 'how many of this small piece fit into the big number?' Multiplying both numbers by the same power of 10 scales them up equally, so the answer never changes — it just becomes an easier whole-number problem.

Quick Tip

To divide by 0.2, you can simply multiply by 5 (since 1 ÷ 0.2 = 5). So 102.84 × 5 = 514.2 — much faster!

Common Mistake

Students often multiply only the dividend (top number) by 10 and forget to multiply the divisor (bottom number) too. This changes the value of the problem and gives a wrong answer.