Solve the Ratio Equation: Converting 1.2:100 to Decimal Form

Q: How many places do I move for different powers of 10?

Count the zeros! Dividing by 10 = 1 place left, by 100 = 2 places left, by 1000 = 3 places left. The number of zeros equals the number of places to move.

Q: Is 1.2:100 the same as 1.2 ÷ 100?

Yes! The colon (:) in ratios means division. So $ 1.2:100 $ is exactly the same as $ 1.2 ÷ 100 $.

Q: How can I check my answer without a calculator?

Use the reverse operation! Since you divided by 100, multiply your answer by 100. If you get back to 1.2, you're correct: $ 0.012 × 100 = 1.2 $ ✓

Decimal Division with Powers of Ten

$1.2:100=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 According to the number of zeros, move the decimal point

00:08 Move the decimal point as many places as there are zeros

00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1.2:100=$

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the given information, which is the number 1.2 and that we need to divide it by 100.
Step 2: Recognize that dividing by 100 means moving the decimal point in 1.2 two places to the left.
Step 3: Shift the decimal point two places to the left in 1.2, resulting in 0.012.

Now, let's work through this solution in detail:

Step 1: We begin with the number 1.2.
Step 2: To divide by 100, visualize the decimal point moving two places left. Since 1.2 is represented as 1.2 (or 1.20 for easier visualization), the decimal point moves past the "1" and an extra zero is added in front:
- Original: 1.2
- First move: 0.12
- Second move: 0.012

Therefore, the solution to the problem is $0.012$ .

Final Answer

$0.012$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by 100 moves decimal point two places left
Technique: From 1.2 → 0.12 → 0.012 when dividing by 100
Check: Multiply answer by 100: 0.012 × 100 = 1.2 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point in wrong direction
Don't move the decimal point to the right when dividing by 100 = 120 instead of 0.012! Division makes numbers smaller, not larger. Always move the decimal point LEFT when dividing by powers of ten.

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 100 move the decimal point left?

Think of it this way: when you divide by 100, you're making the number 100 times smaller. Moving the decimal point left makes numbers smaller, which is exactly what division does!

How many places do I move for different powers of 10?

Count the zeros! Dividing by 10 = 1 place left, by 100 = 2 places left, by 1000 = 3 places left. The number of zeros equals the number of places to move.

What if I don't have enough digits to move the decimal point?

Add zeros in front! For example, if you need to move 1.2 three places left for dividing by 1000, you get $0.0012$ by adding the extra zero.

Is 1.2:100 the same as 1.2 ÷ 100?

Yes! The colon (:) in ratios means division. So $1.2:100$ is exactly the same as $1.2 ÷ 100$ .

How can I check my answer without a calculator?

Use the reverse operation! Since you divided by 100, multiply your answer by 100. If you get back to 1.2, you're correct: $0.012 × 100 = 1.2$ ✓

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