How to Convert Place Values?

Converting between place values is a key aspect of understanding numbers and performing mathematical operations.

How to Convert Place Values?

A step-by-step guide to place values converting

A place value is a digit’s value within a number. For instance, the \(5\) within \(350\) stands for five tens, which is \(50\).

To convert in-between place values, don’t forget these relationships:

one ten \(= 10\) ones

one hundred \(= 10\) tens

one thousand \(= 10\) hundreds

one ten thousand \(= 10\) thousands

One hundred thousand \(= 10\) ten-thousands

The place value system is a way to organize numbers. It is based on the “base 10” system, where each place represents ten times the value of the place to its right. The places in a number, starting from the right, represent the ones, tens, hundreds, thousands, and so on. For example, in the number 1234:

  • 4 is in the ones place.
  • 3 is in the tens place.
  • 2 is in the hundreds place.
  • 1 is in the thousands place.

So, the number 1234 means 1 thousand, 2 hundreds, 3 tens, and 4 ones.

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Now, let’s say you want to convert a number from one place value to another, for example, converting 3 hundreds to tens. Here are the steps:

  1. Identify the place value of the number you’re starting with. In our example, we’re starting with 3 hundreds.
  2. Identify the place value you want to convert to. In our example, we want to convert to tens.
  3. Now, think about the relationship between the two place values. Moving one place to the right (like from hundreds to tens) means multiplying by 10. Moving one place to the left (like from tens to hundreds) means dividing by 10. In our case, we’re moving from hundreds to tens, so we multiply by 10.
  4. Multiply or divide as necessary. In our example, we multiply 3 (hundreds) by 10 to get 30 tens. So, 3 hundreds is the same as 30 tens.

Remember, when you’re working with place values, you’re basically working with powers of 10. Every time you move one place to the right, you’re multiplying by 10. Every time you move one place to the left, you’re dividing by 10.

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Converting place values-Example:

What is the number to fill in the blank?

 \(9\) thousands \(=\) … hundreds

Solution: One thousand \(= 10\) hundreds

So, to find out the number, start counting by tens.

 \(9\) thousands \(= 90\) hundreds

Exercises for Converting Place Values

Fill in the blank.

  1. \(60\) hundreds \(=\) _______ tens
  2. \(3\) hundreds \(=\) _______ tens 
  3. \(7\) ten thousands \(=\) _______ hundreds
  1. \(\color{blue}{600}\)
  2. \(\color{blue}{30}\)
  3. \(\color{blue}{700}\)

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