Solve: 3×100,000 + 9×100 + 8×10 + 1 in Expanded Form

Place Value Addition with Standard Form

3×100,000+9×100+8×10+1×1= 3\times100,000+9\times100+8\times10+1\times1=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

3×100,000+9×100+8×10+1×1= 3\times100,000+9\times100+8\times10+1\times1=

2

Step-by-step solution

To solve the given problem, we need to evaluate the expression step-by-step.

Let's begin by calculating each term in the expression:

  • The first term is 3×100,000 3 \times 100,000 . Calculating this, we get 300,000 300,000 .
  • The second term is 9×100 9 \times 100 . Calculating this, we find 900 900 .
  • The third term is 8×10 8 \times 10 . This results in 80 80 .
  • The fourth term is 1×1 1 \times 1 , which gives 1 1 .

Now, let's sum these calculated values:

300,000+900+80+1 300,000 + 900 + 80 + 1

Let's calculate this step-by-step:

  • 300,000+900=300,900 300,000 + 900 = 300,900
  • 300,900+80=300,980 300,900 + 80 = 300,980
  • Finally, 300,980+1=300,981 300,980 + 1 = 300,981

The result of the expression is 300,981 300,981 .

Given the answer choices, choice 3 300,981 300,981 is indeed the correct one.

Therefore, the solution to the problem is 300,981 300,981 .

3

Final Answer

300,981 300,981

Key Points to Remember

Essential concepts to master this topic
  • Rule: Multiply each digit by its place value before adding
  • Technique: Calculate 3×100,000=300,000 3×100,000 = 300,000 then add remaining terms
  • Check: Sum 300,000 + 900 + 80 + 1 equals 300,981 ✓

Common Mistakes

Avoid these frequent errors
  • Adding coefficients without multiplying by place values
    Don't add 3+9+8+1 = 21 as your final answer! This ignores the place values completely and gives a meaningless result. Always multiply each coefficient by its place value first, then add the products.

Practice Quiz

Test your knowledge with interactive questions

What number do the units shown below represent?

10,0001000111010100011

UnitsTensHundredsThousandsBeforeConversionAfterConversionTens ofThousands

Write the units in the place value chart and convert into a number.

FAQ

Everything you need to know about this question

Why can't I just add 3 + 9 + 8 + 1?

+

Because each number has a different place value! The 3 represents 300,000 (not just 3), the 9 represents 900, the 8 represents 80, and only the 1 represents 1.

What does expanded form mean?

+

Expanded form shows each digit multiplied by its place value. It breaks down a number like 300,981 into 3×100,000+9×100+8×10+1×1 3×100,000 + 9×100 + 8×10 + 1×1 .

How do I know which place value goes with each digit?

+

Start from the right: ones, tens, hundreds, thousands, ten thousands, hundred thousands. The rightmost digit is always in the ones place.

Can I solve this in a different order?

+

Yes! Addition is commutative, so you can add the terms in any order. Just make sure to calculate each multiplication first: 3×100,000 3×100,000 , 9×100 9×100 , etc.

What if there's a zero in the expanded form?

+

If a place value has zero, like 0×1,000 0×1,000 , it equals zero and doesn't affect the sum. You can skip terms with zero coefficients when adding.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Natural numbers up to a million questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations