Solve (1.4-0.3)×10: Decimal Operations with Powers of Ten

Decimal Operations with Order of Operations

(1.40.3)×10= (1.4-0.3)\times10=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Always solve parentheses first
00:07 Use long subtraction
00:14 Multiply and solve
00:17 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

(1.40.3)×10= (1.4-0.3)\times10=

2

Step-by-step solution

According to the order of operations, we will first solve the expression in parentheses.

We will solve the exercise vertically, making sure to align digits properly - ones under ones, tens under tens, and so on. Note that the decimal point is in place:

1.40.3 1.4\\-0.3\\

And we get the result:

1.1 1.1

Now we have the expression:

1.1×10= 1.1\times10=

The above expression doesn't need to be calculated, we simply need to move the decimal point one place to the right, since we are multiplying by ten, meaning we're adding a tens place.

Therefore, we get the result:

11 11

3

Final Answer

11 11

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Always solve parentheses first, then multiplication
  • Decimal Subtraction: Align decimal points: 1.4 - 0.3 = 1.1
  • Check: Verify 1.1 × 10 = 11 by moving decimal right ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations
    Don't multiply 1.4 × 10 first then subtract 0.3 × 10 = 14 - 3 = 11! This gives the wrong process even though the answer happens to match. Always solve parentheses before multiplication following PEMDAS.

Practice Quiz

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\( 140-70= \)

FAQ

Everything you need to know about this question

Why do I solve the parentheses first?

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The order of operations (PEMDAS) requires parentheses first! The expression (1.40.3)×10 (1.4-0.3)\times10 means 'subtract first, then multiply the result.'

How do I subtract decimals like 1.4 - 0.3?

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Line up the decimal points vertically! Write 1.4 above 0.3, making sure the decimal points align. Then subtract normally: 4 - 3 = 1, and 1 - 0 = 1, giving you 1.1.

Is there a shortcut for multiplying by 10?

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Yes! When multiplying a decimal by 10, simply move the decimal point one place to the right. So 1.1×10=11 1.1 \times 10 = 11 (the decimal point moves from 1.1 to 11.0).

What if I get a different answer?

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Double-check your work! Make sure you solved inside the parentheses first, aligned decimal points correctly, and moved the decimal point right when multiplying by 10.

Why isn't the answer 9?

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Getting 9 means you probably calculated 1.40.3=0.9 1.4 - 0.3 = 0.9 instead of 1.1. Remember: when subtracting decimals, 4 - 3 = 1 in the tenths place, and 1 - 0 = 1 in the ones place!

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