Basic 7

Lesson 1:
Multiplication & Division Facts

Lesson 2:
Convert Benchmark Fractions

Lesson 3:
Decimals & Powers of 10

Decimals & Powers of 10

Sometimes we will be required to multiply or divide given decimals by powers of 10, such as 10, 100, 1000, \(\frac{1}{100}\), etc.

In this lesson, we will learn how to multiply and divide various decimals by powers of 10.

Multiplying or dividing by powers of \(10\) is about shifting the decimal point to the right (if it is multiplication) or to the left (when dividing).





Multiplying Decimals by 10, 100, 1000, etc.

When multiplying decimals by powers of 10, the decimal point moves an amount of steps to the right, depending on the number of zeros (0) present in the power of 10.

That is, when you multiply a decimal number by 10, the decimal point moves one place to the right. When you multiply by 100, the decimal point moves two places to the right, and when you multiply by 1000, the decimal point moves three places to the right.

Let's take it one at a time.





MULTIPLYING BY 10


When multiplying a decimal number by 10, move the decimal point one place to the right.

This is because there is only 1 zero (0) present in the number 10

Consider the examples below:





Example 1


Multiply 3.45 by 10


Solution









Example 2


Multiply 105.25 by 10


Solution









Example 3


Multiply 0.67 by 10


Solution









MULTIPLYING BY 100


When multiplying a decimal number by 100, move the decimal point two places to the right.

This is because there are 2 zeros (00) present in the number 100

Consider the examples below:





Example 4


Multiply 3.45 by 100


Solution









Example 5


Multiply 105.25 by 100


Solution









Example 6


Multiply 0.67 by 100


Solution









MULTIPLYING BY 1000


When multiplying a decimal number by 1000, move the decimal point three places to the right.

This is because there are 3 zeros (000) present in the number 1000

Consider the examples below:





Example 7


Multiply 3.45 by 1000


Solution









Example 8


Multiply 105.25 by 1000


Solution









Example 9


Multiply 0.67 by 1000


Solution









Exercise 1

Solve the following:

  1. Multiply 4.56 by 10.

  2. Multiply 0.032 by 100.

  3. Multiply 12.7 by 1000.

  4. Multiply 0.0045 by 10.

  5. Multiply 56.78 by 100.

  6. Multiply 7.001 by 1000.

  7. Multiply 0.89 by \(10^3\).

  8. Multiply 0.0078 by \(10^2\).

  9. Multiply 123.4 by 10.

  10. Multiply 0.056 by \(10^4\).





Dividing Decimals by 10, 100, 1000, etc.

When dividing decimals by powers of 10, the decimal point moves a number of places to the left, depending on the number of zeros (0) present in the power of 10.

That is, when you divide a decimal number by 10, the decimal point moves one place to the left. When you divide by 100, the decimal point moves two places to the left, and when you divide by 1000, the decimal point moves three places to the left.

Let's take it one at a time.





DIVIDING BY 10


Dividing a decimal by 10, is the same as multiplying it by \(\frac{1}{10}\). That is,

\[\frac{a}{10} = a \times \frac{1}{10}\]

When dividing a decimal number by 10, move the decimal point one place to the left. This is because there is only 1 zero (0) present in the number 10.

Consider the examples below:





Example 10


Divide 3.45 by 10


Solution









Example 11


Divide 105.25 by 10


Solution









Example 12


Divide 0.67 by 10


Solution









DIVIDING BY 100


Dividing a decimal by 100, is the same as multiplying it by \(\frac{1}{100}\). That is,

\[\frac{a}{100} = a \times \frac{1}{100}\]

When dividing a decimal number by 100, move the decimal point two places to the left. This is because there are 2 zeros (00) present in the number 100.

Consider the examples below:





Example 13


Divide 3.45 by 100


Solution









Example 14


Divide 105.25 by 100


Solution









Example 15


Divide 0.67 by 100


Solution









DIVIDING BY 1000


Dividing a decimal by 1000, is the same as multiplying it by \(\frac{1}{1000}\). That is,

\[\frac{a}{1000} = a \times \frac{1}{1000}\]

When dividing a decimal number by 1000, move the decimal point three places to the left. This is because there are 3 zeros (000) present in the number 1000.

Consider the examples below:





Example 16


Divide 3.45 by 1000


Solution









Example 17


Divide 105.25 by 1000


Solution









Example 18


Divide 0.67 by 1000


Solution









Exercise 2

Solve the following:

  1. Divide 45.6 by 10.

  2. Divide 789.0 by 100.

  3. Divide 0.345 by 1000.

  4. Divide 12.34 by 10.

  5. Divide 67.89 by 100.

  6. Divide 0.5678 by \(10^3\).

  7. Divide 456 by \(10^2\).

  8. Divide 3.210 by 1000.

  9. Divide 890.12 by 10.

  10. Divide 0.0005 by \(10^4\).





Summary & Special Cases

\(* \ \) When multiplying by powers of 10:

Move the decimal point to the right, depending on the number of zeros present in the power of 10.

\(* \ \) When dividing by powers of 10:

Move the decimal point to the left, depending on the number of zeros present in the power of 10.

\(* \ \) Number of zeros:

The number of zeros in the power of 10 determines how many places you will move the decimal point to the left or right.

\(* \ \) Special Case:

If there are not enough digits to move the decimal point, add zeros as needed.





Example 19


Multiply 0.67 by 100000


Solution









Example 20


Divide 0.067 by 10000


Solution









Exercise 3

Solve the following:

  1. Multiply 5.67 by 100.

  2. Divide 123.45 by 1000.

  3. A water tank holds 567.89 liters. What is the capacity of one tank in deciliters?

  4. Divide 789.0 by 10.

  5. Multiply 0.032 by 1000.

  6. Divide 12.34 by 100.

  7. Multiply 1.23 by \(10^3\).

  8. Divide 45.6 by \(10^2\).

  9. A factory produces 0.05 kilograms of material in one batch. How many kilograms will 1000 batches produce?

  10. If the price of an item is Gh₵ 12.34, what is the price of 10 such items?





Quick Test

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