Solve: 1×100,000 + 5×1,000 + 7×10 + 4×1 in Standard Form

Q: What does 'standard form' mean in this problem?

Standard form means writing the number using our regular decimal number system. You're converting from expanded form (showing place values) to standard form (the final number).

Q: Why do we multiply instead of just adding the numbers?

Each number represents a different place value! The 5 isn't just 5 - it's 5 thousands, which equals 5,000. You must multiply by place value to get the true value of each digit.

Q: How do I keep track of all the zeros when multiplying?

Count the zeros in the place value: 100,000 has 5 zeros, so 1×100,000 = 100,000. For 1,000 (3 zeros), 5×1,000 = 5,000.

Q: What if I get confused about which digit goes where?

Line up your partial products by place value:100,000 (hundred thousands)5,000 (thousands)70 (tens)4 (ones)Then add them together carefully!

Q: How can I check if my final answer makes sense?

Look at the largest place value: 1×100,000 = 100,000. Your final answer should be slightly bigger than 100,000 since you're adding more positive numbers to it.

Place Value Operations with Standard Form

$1\times100,000+5\times1000+7\times10+4\times1=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$1\times100,000+5\times1000+7\times10+4\times1=$

Step-by-step solution

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

Step 1: Perform the multiplication operations for each term.
Step 2: Add the results of the multiplications together to obtain the final result.

Let's perform each step:

Step 1: Execute the multiplications:
- Calculate $1 \times 100,000$ :

This equals $100,000$ .

Step 2: Calculate $5 \times 1,000$ :

This equals $5,000$ .

Step 3: Calculate $7 \times 10$ :

This equals $70$ .

Step 4: Calculate $4 \times 1$ :

This equals $4$ .

Step 5: Add the results from all the multiplications:

$100,000 + 5,000 + 70 + 4 = 105,074$

Therefore, the solution to the problem is $105,074$ .

Final Answer

$105,074$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply each digit by its place value first
Technique: Calculate $1 \times 100,000 = 100,000$ before adding
Check: Count digits in final answer: 105,074 has 6 digits ✓

Common Mistakes

Avoid these frequent errors

Adding coefficients without multiplying by place values
Don't just add 1+5+7+4=17! This ignores place values completely and gives a tiny wrong answer. Always multiply each coefficient by its place value first: 1×100,000 + 5×1,000 + 7×10 + 4×1, then add the results.

Practice Quiz

Test your knowledge with interactive questions

If you use all of the units shown below and place them in the table, then what number do they make?

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

FAQ

Everything you need to know about this question

What does 'standard form' mean in this problem?

Standard form means writing the number using our regular decimal number system. You're converting from expanded form (showing place values) to standard form (the final number).

Why do we multiply instead of just adding the numbers?

Each number represents a different place value! The 5 isn't just 5 - it's 5 thousands, which equals 5,000. You must multiply by place value to get the true value of each digit.

How do I keep track of all the zeros when multiplying?

Count the zeros in the place value: 100,000 has 5 zeros, so 1×100,000 = 100,000. For 1,000 (3 zeros), 5×1,000 = 5,000.

What if I get confused about which digit goes where?

Line up your partial products by place value:

100,000 (hundred thousands)
5,000 (thousands)
70 (tens)
4 (ones)

Then add them together carefully!

How can I check if my final answer makes sense?

Look at the largest place value: 1×100,000 = 100,000. Your final answer should be slightly bigger than 100,000 since you're adding more positive numbers to it.

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