Solve Decimal Multiplication: 0.01 × 0.315 Step-by-Step

Q: Why do I ignore the decimal points at first?

Ignoring decimals initially makes multiplication much easier! You multiply the digits normally (1 × 315 = 315), then use the decimal place rule to position the decimal point correctly.

Q: How do I count decimal places correctly?

Count each digit to the right of the decimal point. $ 0.01 $ has 2 places, $ 0.315 $ has 3 places, so total is 2 + 3 = 5 places.

Q: Can I use a calculator to check my work?

Absolutely! Calculators are great for verification. But learning the manual method helps you understand why $ 0.01 × 0.315 = 0.00315 $ and catch calculator input errors.

Q: What if one number doesn't have a decimal point?

Numbers like 5 actually have zero decimal places (same as 5.0). So 5 × 0.23 would have 0 + 2 = 2 decimal places total.

Decimal Multiplication with Place Value Alignment

$0.01\times0.315=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert from decimal to fraction

00:11 There are 2 zeros in the denominator, so we'll add 2 zeros

00:15 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

$0.01\times0.315=$

Step-by-step solution

To solve the problem $0.01 \times 0.315$ , we'll follow these steps:

Step 1: Multiply the numbers ignoring the decimal points.
Step 2: Place the decimal point in the product according to the combined decimal places in the original numbers.

Let's proceed through each step:

First, multiply the numbers as whole numbers: $1 \times 315 = 315$ .

Next, count the total number of decimal places in the factors. The number $0.01$ has two decimal places, and $0.315$ has three decimal places, adding up to five decimal places.

Therefore, in the product, we need to place the decimal point five places from the right.

Starting from $315$ , we place the decimal point to get $0.00315$ . Since we add three leading zeros to accommodate the five decimal places total.

Thus, the result of $0.01 \times 0.315$ is $0.00315$ .

Final Answer

$0.00315$

Key Points to Remember

Essential concepts to master this topic

Rule: Count total decimal places in both factors to place decimal point
Technique: Multiply 1 × 315 = 315, then place decimal 5 places from right
Check: Verify 0.01 × 0.315 has 2 + 3 = 5 total decimal places ✓

Common Mistakes

Avoid these frequent errors

Adding decimal places instead of multiplying whole numbers first
Don't try to multiply 0.01 × 0.315 with decimals in place = confusing alignment errors! This leads to misplaced decimal points and wrong answers. Always multiply as whole numbers first (1 × 315), then count total decimal places to position the decimal point.

Practice Quiz

Test your knowledge with interactive questions

$0.1 \times 0.008 =$

FAQ

Everything you need to know about this question

Why do I ignore the decimal points at first?

Ignoring decimals initially makes multiplication much easier! You multiply the digits normally (1 × 315 = 315), then use the decimal place rule to position the decimal point correctly.

What if I need to add zeros to my answer?

That's normal! When you need 5 decimal places but only have 3 digits (315), add leading zeros: 0.00315. The zeros are essential for correct place value.

How do I count decimal places correctly?

Count each digit to the right of the decimal point. $0.01$ has 2 places, $0.315$ has 3 places, so total is 2 + 3 = 5 places.

Can I use a calculator to check my work?

Absolutely! Calculators are great for verification. But learning the manual method helps you understand why $0.01 × 0.315 = 0.00315$ and catch calculator input errors.

What if one number doesn't have a decimal point?

Numbers like 5 actually have zero decimal places (same as 5.0). So 5 × 0.23 would have 0 + 2 = 2 decimal places total.

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