Dividing a number by 100 using place value is as simple as shifting each digit two places to the right.
This makes the number 100 times smaller. For a whole number, this means the decimal point, which is typically unseen at the end of the number, moves two spaces to the left.
Understanding the concept
Place value is the value of each digit in a number based on its position. In a number like 453, the '4' is in the hundreds place, the '5' in the tens place, and the '3' in the ones (or units) place. Each position is 10 times larger than the one to its right.
Division and place value
When you divide a number by a power of 10, you are making its value smaller. Dividing by 10 makes a number 10 times smaller, so each digit moves one place to the right. Since 100 is 10×1010 cross 10
10×10
, dividing by 100 is the same as dividing by 10 twice. This results in each digit shifting two places to the right.
How to divide by 100 using place value
Step 1: Identify the decimal point
If you are dividing a whole number, the decimal point is invisible and located at the end of the number.
- Example: 453
- Think of it as 453.
Step 2: Shift the decimal point
Move the decimal point two places to the left. The number of places you shift is equal to the number of zeros in 100.
- Example: 453
- Start: 453.
- Shift 1 place left: 45.3
- Shift 2 places left: 4.53
Step 3: Add placeholders if needed
If there are not enough digits to the left of the decimal point, you must add zeros as placeholders.
- Example: 6 ÷ 100
- Start with the decimal point: 6.
- Shift 1 place left: .6
- Shift 2 places left: .06
- Add a zero in the ones place for clarity: 0.06
Practice with more examples
Dividing a whole number
**Problem: 381÷100381 divided by 100
381÷100**
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Original number: 381
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Shift the decimal: Move the decimal point (at the end) two places to the left.381.→3.81381. right arrow 3.81
381.→3.81
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Answer: 3.81
Dividing a number with a decimal
**Problem: 45.9÷10045.9 divided by 100
45.9÷100**
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Original number: 45.9
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Shift the decimal: Move the decimal point two places to the left.45.9→0.45945.9 right arrow 0.459
45.9→0.459
-
Answer: 0.459
Dividing a smaller number by 100
**Problem: 7÷1007 divided by 100
7÷100**
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Original number: 7
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Shift the decimal: Move the decimal point (at the end) two places to the left, adding placeholders.7.→.07→0.077. right arrow .07 right arrow 0.07
7.→.07→0.07
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Answer: 0.07
Why does this method work?
This method is a shortcut that works because of our base-10 number system.
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The division operation reduces the value of a number.
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In a place value system, moving digits to the right reduces their value.
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Dividing by 100 reduces a number's value by a factor of 100.
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Moving digits two places to the right also reduces their value by a factor of 100 (once for each place, or 10×1010 cross 10
10×10
).
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For example, the digit '3' in 300 has a value of 300. When you divide by 100, that same digit '3' is now in the ones place, with a value of 3. You can see how the digit moved two places to the right and its value was reduced by 100.