I. Multiplying or dividing an integer by 10, 100, or 1,000
A. Multiplying by 10, 100, or 1,000
We know that:
54 tens are made up of 540 units;
54 hundreds are made up of 5,400 units;
54 thousands are made up of 54,000 units.
So we can write that:
54 × 10 = 10 × 54 = 540
54 × 100 = 100 × 54 = 5,400
54 × 1,000 = 1000 × 54 = 54,000
General rule: To write the result of multiplying an integer by 10, 100, or 1,000, simply imagine a decimal point to the right of the units figure and move it respectively one, two, or three places to the right.
B. Dividing by 10, 100, or 1,000
We know that:
54 tenths are
54 hundredths are
54 thousandths are
So we can write that:
54 ÷ 10 = 5.4
54 ÷ 100 = 0.54
54 ÷ 1,000 = 0.054
As we know that 54 = 54.0, we can take 5.4, 0.54, and 0.054 as being the result of moving the decimal point in 54.0 one, two, or three places to the left.
General rule: To write the result of dividing an integer by 10, 100, or 1,000, simply imagine a decimal point to the right of the units figure and move it respectively one, two, or three places to the left.
II. Multiplying or dividing a decimal by 10, 100, or 1,000
A. Multiplying by 10, 100, or 1,000
We know that:
So we can work out that:
4.5 × 10 = 10 × 4.5 = 45
4.5 × 100 = 100 × 4.5 = 450
4.5 × 1,000 = 1,000 × 4.5 = 4,500
General rule: To write the result of multiplying a decimal that is not an integer by 10, 100, or 1,000, simply move the decimal point respectively one, two, or three places to the right.
B. Dividing by 10, 100, or 1,000
As with division of an integer by 10, 100, or 1,000, we can write that:
4.5 ÷ 10 = 0.45
4.5 ÷ 100 = 0.045
4.5 ÷ 1,000 = 0.0045
General rule: To write the result of dividing a decimal that is not an integer by 10, 100, or 1,000, simply move the decimal point respectively one, two, or three places to the left.
III. Multiplying or dividing a decimal by 0.1, 0.01, or 0.001
A. Multiplying a number by 0.1, 0.01, or 0.001
Multiplying a number by 0.1 is the same as dividing it by 10.
Multiplying a number by 0.01 is the same as dividing it by 100.
Multiplying a number by 0.001 is the same as dividing it by 1,000.
Examples:
89.5 × 0.1 = 89.5 ÷ 10 = 8.95
89.5 × 0.01 = 89.5 ÷ 100 = 0.895
89.5 × 0.001 = 89.5 ÷ 1,000 = 0.0895
B. Dividing a number by 0.1, 0.01, or 0.001
Dividing a number by 0.1 is the same as multiplying it by 10.
Dividing a number by 0.01 is the same as multiplying it by 100.
Dividing a number by 0.001 is the same as multiplying it by 1,000.
Examples:
6.04 ÷ 0.1 = 6.04 × 10 = 60.4
6.04 ÷ 0.01 = 6.04 × 100 = 604
6.04 ÷ 0.001 = 6.04 × 1,000 = 6,040
Read more:
Reading and Writing Decimal Numbers
Multiplying Decimal Numbers
Dividing Decimal Numbers
Converting Decimals to Fractions
The Effect of Addition and Multiplication on the Order of Numbers
Describing Different Types of Numbers
Dividing Whole Numbers with a Remainder
Comparing and Ordering Decimal Numbers
Adding and Subtracting Decimal Numbers