Number Formation: Creating the Six-Digit Number 900,999

Q: Why don't we write the ten-thousands and thousands places?

Because 900,999 has zeros in those positions! The number is 9-0-0-9-9-9, so we only include places where we actually have non-zero digits.

Q: How do I know which place value each digit represents?

Start from the right and work left: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands. Each position is 10 times bigger than the one to its right!

Q: What if I accidentally include a zero place value?

Your final answer will be too big! For example, including 9×10,000 would add an extra 90,000 to your total, giving you 990,999 instead of 900,999.

Q: Is there a pattern to the place values?

Yes! Each place value is a power of 10: $ 10^0 = 1, 10^1 = 10, 10^2 = 100, 10^3 = 1,000 $, and so on. This makes it easier to remember!

Place Value Decomposition with Six-Digit Numbers

Choose the correct exercise to attain the number 900,999.

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Step-by-step written solution

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Understand the problem

Choose the correct exercise to attain the number 900,999.

Step-by-step solution

To solve this problem, let's consider the number $900,999$ . This number can be broken down as follows:

The '900,000' component can be written as $9 \times 100,000$ , as 900,000 is nine hundred thousands.
The '999' component can be broken into $9 \times 100 + 9 \times 10 + 9 \times 1$ , representing nine hundreds, nine tens, and nine units.

Now, combining these parts together, the exercise becomes:

$9 \times 100,000 + 9 \times 100 + 9 \times 10 + 9 \times 1 = 900,999$ .

This is the decomposition that accurately reflects the number $900,999$ .

Thus the correct choice among the options provided is: $9 \times 100,000 + 9 \times 100 + 9 \times 10 + 9 \times 1 = 900,999$ .

Final Answer

$9\times100,000+9\times100+9\times10+9\times1=900,999$

Key Points to Remember

Essential concepts to master this topic

Place Value Rule: Each digit's value equals digit times its place value position
Technique: Break down 900,999 = 9×100,000 + 0×10,000 + 0×1,000 + 9×100 + 9×10 + 9×1
Check: Add all products: 900,000 + 0 + 0 + 900 + 90 + 9 = 900,999 ✓

Common Mistakes

Avoid these frequent errors

Including zero place values in decomposition
Don't write 9×10,000 + 9×1,000 when those positions have zeros = adding values that aren't there! This inflates your number beyond the target. Always include only the place values where digits actually appear as non-zero.

Practice Quiz

Test your knowledge with interactive questions

What number do the units shown below represent?

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

FAQ

Everything you need to know about this question

Why don't we write the ten-thousands and thousands places?

Because 900,999 has zeros in those positions! The number is 9-0-0-9-9-9, so we only include places where we actually have non-zero digits.

How do I know which place value each digit represents?

Start from the right and work left: ones, tens, hundreds, thousands, ten-thousands, hundred-thousands. Each position is 10 times bigger than the one to its right!

What if I accidentally include a zero place value?

Your final answer will be too big! For example, including 9×10,000 would add an extra 90,000 to your total, giving you 990,999 instead of 900,999.

Is there a pattern to the place values?

Yes! Each place value is a power of 10: $10^0 = 1, 10^1 = 10, 10^2 = 100, 10^3 = 1,000$ , and so on. This makes it easier to remember!

How can I check my decomposition quickly?

Add up all your products and see if you get the original number. If 900,000 + 900 + 90 + 9 = 900,999, you're correct!

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