# DIVIDING DECIMALS by 10 100 and 1000

Consider the decimal number 25.86.

Let us divide 25.86 by 10.

= 25.86/10

Whenever a decimal number is divided by 10, the decimal point has to moved to left by one digit.

= 2.586

In the similar manner, we can find the results, when a decimal number is divided by 100, 1000, etc.,

For example, let us divide 385.6 by 100.

= 385.6/100

Since we divide 385.6 by 100, the decimal point has to be moved to the left by two digits.

= 3.856

Evaluate :

1597.8 ÷ 1000

Here, 15978 is divided by 1000. So, the decimal point has to be moved to the left by three digits.

1597.8 ÷ 1000 = 1.5978

## Summary

÷ by 10 ----> Move '.' 1 digit to the left

÷ by 100 ----> Move '.' 2 digits to the left

÷ by 1000 ----> Move '.' 3 digits to the left

÷ by 10000 ----> Move '.' 4 digits to the left

What if the given number is a whole number (without decimal point?

If the given number is a whole number (no decimal point), assume that there is a decimal at the end of the number.

For example, let us divide the whole number 35 by 10.

Assume there is decimal point in 35 at the end.

35 ÷ 10 = 35. ÷ 10

Since 35. is divided by 10, move the decimal point to the left by one digit.

35 ÷ 10 = 3.5

In other words, when a whole number is divided by 10, take the decimal point such that there is one digit to the right of it.

If a whole number is divided by 100, take the decimal point such that there are two digits to the right of the decimal point.

## Solved Problems

Problem 1 :

Evaluate :

38.6 ÷ 10

Solution :

Since 38.6 is divided by 10, move the decimal point to the left by one digit.

38.6 ÷ 10 = 3.86

Problem 2 :

Evaluate :

592.7 ÷ 100

Solution :

Since 592.7 is divided by 100, move the decimal point to the left by two digits.

592.7 ÷ 100 = 5.927

Problem 3 :

Evaluate :

72015.6 ÷ 1000

Solution :

Since 72015.6 is divided by 1000, move the decimal point to the left by three digits.

72015.6 ÷ 1000 = 72.0156

Problem 4 :

Evaluate :

29105.4 ÷ 10000

Solution :

Since 29105.4 is divided by 10000, move the decimal point to the left by four digits.

29105.4 ÷ 10000 = 2.91054

Problem 5 :

Evaluate :

23 ÷ 10

Solution :

Here 23 is divided by 10 and 23 is a whole number.

Since 23 is divided by 10, take decimal point in 23 such that there is one digit to the right of the decimal point.

23 ÷ 10 = 2.3

Problem 6 :

Evaluate :

5 ÷ 10

Solution :

Here 5 is divided by 10 and 5 is a whole number.

Since 5 is divided by 10, take decimal point in 5 such that there is one digit to the right of the decimal point.

5 ÷ 10 = 0.5

Problem 7 :

Evaluate :

49 ÷ 100

Solution :

Here 49 is divided by 100 and 49 is a whole number.

Since 49 is divided by 100, take decimal point in 49 such that there are two digits to the right of the decimal point.

49 ÷ 100 = 0.49

Problem 8 :

Evaluate :

3.5 ÷ 100

Solution :

Since 49 is divided by 100, decimal point has to be moved to the left by two digits. But, there is only one digit to the left of the decimal point. To get one more digit, add one zero.

3.5 ÷ 100 = 0.035

Problem 9 :

Evaluate :

0.7 ÷ 10

Solution :

Since 0.7 is divided by 10, decimal point has to be moved to the left by one digit. But, there is no digit to the left of the decimal point. To get one digit, add one zero.

0.7 ÷ 10 = 0.07

Problem 10 :

Evaluate :

0.03 ÷ 1000

Solution :

Since 0.03 is divided by 1000, decimal point has to be moved to the left by three digits. But, there is no digit to the left of the decimal point. To get three digits, add three zeros.

0.03 ÷ 1000 = 0.00003

Problem 11 :

The total cost of 10 fruits is \$42.50. Find the cost of one fruit.

Solution :

To find the cost of one fruit, divide the total cost of 10 fruits by 10.

= 42.50/10

= 42.5 ÷ 10

= ⁴²⁵⁄₁₀ ÷ ¹⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁄₁.

= ⁴²⁵⁄₁₀ x

⁴²⁵⁄₁₀₀

425 is a whole number. Since 425 is divided by 100, take decimal point in 429 such that there are two digits to the right of the decimal point.

= 4.25

The cost of one fruit is \$4.25.

Problem 12 :

Mr. Lenin person walks regularly in the morning. If he walks 4283.6 ft. in 100 minutes, find his speed in ft. per minute.

Solution :

Formula to find speed :

Speed = Distance/Time

= 4283.6/100

= 4283.6 ÷ 100

⁴²⁸³⁶⁄₁₀ ÷ ¹⁰⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁰⁄₁.

⁴²⁸³⁶⁄₁₀ x ¹⁄₁₀₀

⁴²⁸³⁶⁄₁₀₀₀

42836 is a whole number. Since 42836 is divided by 1000, take decimal point in 42836 such that there are three digits to the right of the decimal point.

= 42.836

The walking speed of Mr. Lenin is 42.836 ft. per minute.

Problem 13 :

A car covers a distance of 73.5 miles in 1 hour 40 minutes. Find the speed of the car in miles per  minute.

Solution :

The time 1 hour 40 minutes is in two units, hours and minutes. Convert it to hours completely.

1 hour 40 minutes = (1 x 60) minutes + 40 minutes

= 60 minutes + 40 minutes

= 100 minutes

Given : 73.5 miles of distance covered in 1 hour 15 minutes.

1 hour 40 minutes ----> 73.5 miles

100 minutes ----> 73.5 miles

1 minute ----> (73.5/100) miles

= 73.5/100

= 73.5 ÷ 100

⁷³⁵⁄₁₀ ÷ ¹⁰⁰⁄₁

Change the division to multiplication by taking reciprocal of ¹⁰⁰⁄₁.

⁷³⁵⁄₁₀ x ¹⁄₁₀₀

⁷³⁵⁄₁₀₀₀

735 is a whole number. Since 735 is divided by 1000, take decimal point in 735 such that there are three digits to the right of the decimal point.

= 0.735

Speed of the car is 0.735 miles per  minute.

Problem 14 :

When the decimal number 2K5.8 is divided by 100, the answer is 2.758. Find the value of K.

Solution :

When the decimal number 2K5.8  is divided by 100, the decimal point has to be moved to the left by two digits.

2K5.8 ÷ 100 = 2.K58 ----(1)

Given : Dividing 2K5.8 by 100 results 2.758.

2K5.8 ÷ 100 = 2.758 ----(2)

Comparing (1) and (2),

2.K58 = 2.758

In the equality of two decimal numbers above, comparing the digits at tenths places,

K = 7

## Practice Questions

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