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To solve this problem, we'll follow these steps:
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:
\( \text{0}.07\times10= \)
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!
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!
Yes! You can set up as long division. But recognizing the decimal shift pattern is much faster for numbers with lots of zeros.
Multiply backwards: 0.051 × 200. Since 0.051 × 200 = 10.2, your answer is right! Always verify by doing the opposite operation.
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.
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