Solve Division Problem: 10.2 ÷ 200 Step by Step

Division Operations with Large Divisors

10.2:200= 10.2:200=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Let's reduce as much as possible
00:24 According to the number of zeros in the denominator, we'll move the decimal point
00:38 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

10.2:200= 10.2:200=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Understand the division involved by recognizing the division problem 10.2200 \frac{10.2}{200} .
  • Step 2: Simplify the division by recognizing how division by 200 affects the decimal point.
  • Step 3: Perform the calculation step-by-step by treating the division as a decimal operation.

Let's address each step:

Step 1: We need to divide 10.2 by 200. This can be viewed as scaling down 10.2 by a factor of 200.

Step 2: When dividing by a number like 200, one approach is to consider how the decimal point will shift. Each "zero" in the divisor typically implies moving the decimal point in the dividend to the left. Since 200 is effectively 2 followed by two zeros, dividing by 200 means moving the decimal point two places to the left in the number 10.2.

Step-by-step:

1. Take 10.2 as the original number.

2. Move the decimal point two places to the left because you are dividing by 200 (equivalent to dividing by 100 then 2, which means two decimal places move).

3. As you move the decimal point in 10.2 to the left, you start by moving from after the "0" in "10.2", resulting in 0.102, and then move it one more spot to obtain 0.051.

Step 3: Therefore, the solution to the problem is:

0.051 0.051

3

Final Answer

0.051 \text{0}.051

Key Points to Remember

Essential concepts to master this topic
  • Rule: Dividing by 200 moves decimal point two places left
  • Technique: 10.2 ÷ 200 = 0.102 ÷ 2 = 0.051
  • Check: Multiply back: 0.051 × 200 = 10.2 ✓

Common Mistakes

Avoid these frequent errors
  • Moving decimal point wrong direction or wrong number of places
    Don't move the decimal point right when dividing by large numbers = answer way too big! This happens when students confuse multiplication with division rules. Always move the decimal point left when dividing by numbers with zeros.

Practice Quiz

Test your knowledge with interactive questions

\( \text{0}.07\times10= \)

FAQ

Everything you need to know about this question

Why does dividing by 200 move the decimal two places left?

+

Think of 200 as 2 × 100. Dividing by 100 moves the decimal point two places left, then dividing by 2 gives you the final answer. It's like scaling down the number!

What if I get confused about which direction to move the decimal?

+

Remember: division makes numbers smaller (except when dividing by numbers less than 1). So 10.2 ÷ 200 must give you something much smaller than 10.2!

Can I just do regular long division instead?

+

Yes! You can set up 10.2200 \frac{10.2}{200} as long division. But recognizing the decimal shift pattern is much faster for numbers with lots of zeros.

How do I check if 0.051 is really correct?

+

Multiply backwards: 0.051 × 200. Since 0.051 × 200 = 10.2, your answer is right! Always verify by doing the opposite operation.

What if my calculator shows a different answer?

+

Double-check your calculator input! Make sure you entered 10.2 ÷ 200, not 102 ÷ 200 or 10.2 ÷ 20. Small typos can give very different results.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Advanced questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations