Solve Decimal Division: 1.71 ÷ 10 Step by Step

Q: Why does dividing by 10 move the decimal point left?

Division makes numbers smaller, so the decimal point moves toward zero. Think of it this way: $ 1.71 ÷ 10 $ means "what number times 10 equals 1.71?" That number must be smaller than 1.71!

Q: What if I need to divide by 100 or 1000?

The pattern continues! Dividing by 100 moves the decimal point 2 places left, and dividing by 1000 moves it 3 places left. Count the zeros to know how many places to move.

Q: Do I need to add zeros when moving the decimal point?

Yes! If moving left creates empty spaces, fill them with zeros. For example: $ 5 ÷ 100 = 0.05 $ (added a zero before the 5).

Q: How can I check my answer without multiplying?

Use estimation! Since $ 1.71 ÷ 10 $ should be about one-tenth of 1.71, look for an answer close to 0.17. The answer 0.171 makes sense!

Q: What's the difference between ÷ and the colon symbol (:)?

They mean exactly the same thing! Both $ 1.71 ÷ 10 $ and $ 1.71:10 $ represent division. The colon is commonly used in some countries and textbooks.

Decimal Division with Powers of Ten

$1.71:10=$

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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 according to the number of zeros

00:16 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

$1.71:10=$

Step-by-step solution

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

Step 1: Understand decimal division by powers of ten.
Step 2: Perform the decimal point shift.
Step 3: Compare the result with the provided options.

Now, let's work through each step:

Step 1: The operation involves division by $10$ , which is equivalent to shifting the decimal point of the number one place to the left. We begin with the number $1.71$ .

Step 2: In $1.71$ , the decimal point is moved one place to the left, changing it to $0.171$ .

Step 3: Check this answer against the options given:

Option 1: $0.17$
Option 2: $0.71$
Option 3: $0.171$
Option 4: $0.711$

The correct answer is Option 3: $0.171$ .

Therefore, the solution to the problem is $0.171$ .

Final Answer

$0.171$

Key Points to Remember

Essential concepts to master this topic

Rule: Dividing by 10 shifts decimal point one place left
Technique: Move 1.71's decimal point left: 1.71 becomes 0.171
Check: Multiply result by 10: 0.171 × 10 = 1.71 ✓

Common Mistakes

Avoid these frequent errors

Moving decimal point the wrong direction
Don't move the decimal point right when dividing by 10 = getting 17.1 instead of 0.171! This makes the number larger instead of smaller. 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 10 move the decimal point left?

Division makes numbers smaller, so the decimal point moves toward zero. Think of it this way: $1.71 ÷ 10$ means "what number times 10 equals 1.71?" That number must be smaller than 1.71!

What if I need to divide by 100 or 1000?

The pattern continues! Dividing by 100 moves the decimal point 2 places left, and dividing by 1000 moves it 3 places left. Count the zeros to know how many places to move.

Do I need to add zeros when moving the decimal point?

Yes! If moving left creates empty spaces, fill them with zeros. For example: $5 ÷ 100 = 0.05$ (added a zero before the 5).

How can I check my answer without multiplying?

Use estimation! Since $1.71 ÷ 10$ should be about one-tenth of 1.71, look for an answer close to 0.17. The answer 0.171 makes sense!

What's the difference between ÷ and the colon symbol (:)?

They mean exactly the same thing! Both $1.71 ÷ 10$ and $1.71:10$ represent division. The colon is commonly used in some countries and textbooks.

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