Moving Decimal Point in 512.415: Finding the Thousandths Position

Q: What's the difference between tenths, hundredths, and thousandths?

These are the first three places after the decimal point:Tenths: 1st place after decimal $10^{-1}$Hundredths: 2nd place after decimal $10^{-2}$Thousandths: 3rd place after decimal $10^{-3}$

Q: Why does moving the decimal point 2 places left work?

In 512.415, the digit 4 is in the tenths place (1st after decimal). To get to the thousandths place (3rd after decimal), it needs to move 2 positions to the right relative to the decimal point. So we move the decimal point 2 places left!

Decimal Place Values with Position Changes

How many places to the left should the decimal point be moved in the number 512.415 in order that the 4 becomes the thousandths digit?

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Step-by-step written solution

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Understand the problem

How many places to the left should the decimal point be moved in the number 512.415 in order that the 4 becomes the thousandths digit?

Step-by-step solution

To solve this problem, we need to reposition the decimal point such that the digit '4' becomes the thousandths digit.

Currently, the number is 512.415. Let's analyze what each digit represents:

The '5' is in the hundreds place.
The '1' is in the tens place.
The '2' is in the ones place.
The '4' is in the tenths place.
The '1' is in the hundredths place.
The '5' is in the thousandths place.

The digit '4' is initially in the tenths place. We want to move it to the thousandths place.

To make '4' the thousandths digit, consider the placement relative to the decimal point. The decimal place values are as follows: tenths ( $10^{-1}$ ), hundredths ( $10^{-2}$ ), thousandths ( $10^{-3}$ ).

Currently, '4' is at the tenths position. By moving the decimal point two places to the left, '4' will become the thousandths digit. The new number arrangement is $5.12415$ .

Thus, the decimal point must be moved 2 places to the left.

The correct answer is $\boxed{2}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Place Values: Tenths, hundredths, thousandths follow powers of 10
Moving Left: Each left move increases place value by factor of 10
Check Position: Count digits after decimal point to verify new position ✓

Common Mistakes

Avoid these frequent errors

Confusing direction of decimal point movement
Don't move the decimal point right when you need the digit to move to a smaller place value = completely wrong answer! Moving right makes digits represent larger values, not smaller ones. Always move the decimal point left to make a digit represent a smaller place value like thousandths.

Practice Quiz

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Determine the numerical value of the shaded area:

FAQ

Everything you need to know about this question

How do I remember which direction to move the decimal point?

Think about what you want the digit to become! If you want a digit to move to a smaller place value (like from tenths to thousandths), move the decimal point left. The digit stays in the same spot, but the decimal point moves!

What's the difference between tenths, hundredths, and thousandths?

These are the first three places after the decimal point:

Tenths: 1st place after decimal $10^{-1}$
Hundredths: 2nd place after decimal $10^{-2}$
Thousandths: 3rd place after decimal $10^{-3}$

Why does moving the decimal point 2 places left work?

In 512.415, the digit 4 is in the tenths place (1st after decimal). To get to the thousandths place (3rd after decimal), it needs to move 2 positions to the right relative to the decimal point. So we move the decimal point 2 places left!

How can I double-check my answer?

Write out the new number and count the positions after the decimal point. In $5.12415$ , count: 1st digit is 1, 2nd digit is 2, 3rd digit is 4 - that's the thousandths position! ✓

What if the number becomes smaller than 1?

That's perfectly normal! When you move the decimal point left enough, you'll get numbers like 0.512415. The important thing is getting the target digit in the correct place value position.

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