Decimal Movement in 512.4156: Positioning 6 in Hundredths Place

Decimal Place Values with Point Movement


How many places to the right should the decimal point be moved in the number 512.4156 in order that the 6 becomes the hundredths digit?

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Step-by-step written solution

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1

Understand the problem


How many places to the right should the decimal point be moved in the number 512.4156 in order that the 6 becomes the hundredths digit?

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Step-by-step solution

We are tasked with moving the decimal point so that '6' occupies the hundredths place. Here’s how we accomplish this:

  • Currently, the number is 512.4156. The placement of digits relative to the decimal point is important.
  • The '6' is initially the fourth digit to the right of the decimal:
    512.4156, where '6' is in the 10410^{-4} place (ten thousandths place).
  • The hundredths place is the second digit to the right of the decimal point.
  • First, move the decimal from 512.4156 to 5124.156. This places '6' in the tenths place.
  • Next, move the decimal again from 5124.156 to 51241.56. This sets '6' in the hundredths place.

Hence, we moved the decimal point 2 places to the right. The correct answer is 2 2 .

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Place Values: Decimal positions follow tenths, hundredths, thousandths, ten thousandths
  • Counting: From 512.4156, digit 6 starts in ten thousandths place
  • Verification: After moving 2 places right, 51241.56 has 6 in hundredths ✓

Common Mistakes

Avoid these frequent errors
  • Counting decimal places from the wrong direction
    Don't count from left to right or start from the wrong position = wrong answer! This leads to moving the decimal point too many or too few places. Always count places from the decimal point going right: first is tenths, second is hundredths.

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 the order of decimal place values?

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Use the pattern: tenths, hundredths, thousandths, ten thousandths. Each place is 10 times smaller than the one before it, just like whole number places but in reverse!

What happens to the number when I move the decimal point?

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Moving the decimal point right makes the number larger, while moving it left makes it smaller. The digits stay the same, but their place values change.

How do I know which direction to move the decimal?

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Think about where the digit needs to go! If it needs to move to a place closer to the decimal point (like from ten thousandths to hundredths), move the decimal right.

Can I just count the places without moving the decimal step by step?

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Yes! Count how many places the digit needs to jump left to reach the hundredths place. In 512.4156, the 6 needs to jump 2 places left, so move decimal 2 places right.

What if moving the decimal creates a very large number?

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That's normal! The question asks for the decimal movement, not whether the final number makes practical sense. Focus on where the specific digit lands.

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