Introduction

Remember that to multiply a decimal by 10, we shift the decimal point one space to the right.

So, to divide a decimal by 10, we shift the decimal point one place to the left.

To demonstrate, let's use this method to find the value of

38.7 \div 10.

First, we write down our number. We can attach as many leading zeros as we want to the whole number part:

Now, we count the zeros in 10. Since 10 contains 1 zero, we move the decimal point 1 place to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 3.87

Therefore: 38.7 \div 10 = 3.87

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Example: Dividing a Number by Ten

Calculate 256 \div 10 .

EXPLANATION

First, we write down our number. We can attach as many leading zeros to the whole number part as we want:

Now, we count the zeros in 10. Since 10 contains 1 zero, we move the decimal point 1 place to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 25.60 = 25.6

Therefore:

256 \div 10 = 25.6

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Practice: Dividing a Number by Ten

$10.8 \div 10 =$

a
 $1.08$
b
 $10$
c
 $108$
d
 $1.8$
e
 $1$
Practice: Dividing a Number by Ten

$32.28 \div 10 =$

a
 $322.8$
b
 $3$
c
 $3,228$
d
 $3.228$
e
 $323$
Example: Dividing a Number Smaller Than Ten by Ten

Calculate 8 \div 10 .

EXPLANATION

First, we write down our number. We can attach as many leading zeros to the whole number part as we want:

Now, we count the zeros in 10. Since 10 contains 1 zero, we move the decimal point 1 place to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 0.80 = 0.8

Therefore:

8 \div 10 = 0.8

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Practice: Dividing a Number Smaller Than Ten by Ten

$3 \div 10 =$

a
 $0.3$
b
 $3$
c
 $0.03$
d
 $30$
e
 $300$
Practice: Dividing a Number Smaller Than Ten by Ten

$0.7 \div 10 =$

a
 $7$
b
 $70$
c
 $0.7$
d
 $0.07$
e
 $0.007$
Dividing Decimals by Larger Powers of Ten

To divide a decimal by a larger power of 10, we shift the decimal point to the left by one place for each zero in the power of 10.

To illustrate, let's use this method to find the value of

9 \div 100.

First, we write down our number. We can attach as many trailing zeros as we want to the whole number part.

Now, we count the zeros in 100. Since 100 contains 2 zeros, we move the decimal point 2 places to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 0.090 = 0.09

Therefore: 9 \div 100 = 0.09

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Example: Dividing a Number by One Hundred

Calculate 66.3 \div 100.

EXPLANATION

First, we write down our number. We can attach as many leading zeros to the whole number part as we want:

Now, we count the zeros in 100. Since 100 contains 2 zeros, we move the decimal point 2 places to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 0.663

Therefore: 66.3 \div 100 = 0.663

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Practice: Dividing a Number by One Hundred

$604 \div 100 =$

a
 $0.604$
b
 $6.04$
c
 $64$
d
 $0.64$
e
 $6.4$
Practice: Dividing a Number by One Hundred

$9.1 \div 100 =$

a
 $0.091$
b
 $0.91$
c
 $1.9$
d
 $0.019$
e
 $0.19$
Example: Dividing a Number by One Thousand

Find the value of 769 \div 1,000 .

EXPLANATION

First, we write down our number. We can attach as many leading zeros to the whole number part as we want:

Now, we count the zeros in 1,000. Since 1,000 contains 3 zeros, we move the decimal point 3 places to the left:

This gives the following diagram:

We ignore the leading zeros in the whole number part and trailing zeros in the decimal part. This gives the following number: 0.7690 = 0.769

Therefore: 769 \div 1,000 = 0.769

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Practice: Dividing a Number by One Thousand

$3 \div 1,000 =$

a
 $300$
b
 $0.3$
c
 $30$
d
 $0.03$
e
 $0.003$
Practice: Dividing a Number by One Thousand

$0.32 \div 1,000 =$

a
 $3.2$
b
 $0.0032$
c
 $0.000\,32$
d
 $320$
e
 $0.032$
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